City captain Silva made his 400th appearance for the Premier League champions in the 3-1 south-coast success, while club-record scorer Aguero claimed his 400th career goal.
Former Spain midfielder Silva marked his occasion by providing two assists, the second of which led to Aguero’s landmark strike, the Argentinian’s second goal of the afternoon.
The victory returned City to winning ways after last weekend’s frustrating 2-2 draw with Tottenham, prompting manager Guardiola to pay tribute to two of his leading performers.
“What can I say, everybody knows him,” Guardiola said of 33-year-old Silva to the club website. “He has a sense, to move between the lines like nobody else in the world – he is a fighter.
“And Sergio, you know his sense of goals in the box is unique in the world.”
Kyle Walker was perhaps fortunate to remain on the field following two poor challenges on Nathan Ake which yielded a single yellow card, before Aguero slotted the visitors ahead following Kevin De Bruyne’s scuffed effort.
In-form Raheem Sterling doubled the advantage with his fifth top-flight goal of the campaign and, despite Cherries substitute Harry Wilson halving the deficit with a superb free-kick, Aguero’s 400th strike for club and country sealed the three points.
It was also a memorable day for midfielder De Bruyne, who, in inadvertent fashion, set a new record as the player to reach 50 Premier League assists in the fewest number of games.
The Belgian required just 123 outings to achieve the feat, 18 fewer than Arsenal’s Mesut Ozil.
Aguero, who has scored 235 of his 400 career goals for City, was full of praise for creative team-mates De Bruyne and Silva.
“Congratulations to Kevin. We know Kevin. He is an amazing player,” said the 31-year-old. “He and David, their assists are so good. We are happy because they play for us.”
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Newcastle United manager Steve Bruce jokingly offered England’s Ashes hero Ben Stokes the chance to play centre-back for the Premier League side after their 1-0 win over Tottenham on Sunday.
Bruce was talking after his side’s hard-earned win in north London and revealed he watched the end of Stokes’s epic Ashes innings against Australia at Headingley that earned England a stunning third Test victory against all the odds.
Newcastle had their own tense ending as they held on for their first victory since Bruce took over at the Tyneside club.
“I don’t know what was more nervous the last 10 minutes of the cricket, but certainly Ben Stokes can come and play centre-half for us next week that’s for sure. How wonderful it was to watch I have to say,” said Bruce.
New Brazilian striker Joelinton scored the only goal against Spurs in what was a superb performance by the visitors, who were the better side overall. And Bruce said of his side’s victory: “I was delighted for me staff and the players in particular.
“They’re a great side Spurs with great players, a great manager, arguably as good as there is. Then to come and turn them over was a big thing for all of us.”
Mauricio Pochettino says his squad is the most unsettled it has ever been in his five years in charge of Tottenham and he still does not know whether Christian Eriksen will stay at the club.
The futures of a number of his players – notably Eriksen – remain in doubt with just over a week before the European transfer window closes.
The Dane, who was on the bench for Sunday’s 1-0 home defeat to Newcastle, has said he wants to leave and his situation is most unclear, with the club likely to sell if a big enough offer comes in.
Jan Vertonghen, in the final year of his contract, has not played at all this season while Toby Alderweireld is also a free agent in the summer. Danny Rose was told he could find himself a new club before the campaign began and Victor Wanyama has been linked with a move to Belgium.
It has left Pochettino complaining of it causing a “mess” at his club as he counts down until September 2.
“You know very well and I told you in pre-season, before (the first game against) Aston Villa, after Aston Villa, positive result or negative result, the group is still unsettled,” he said.
“We need to find solutions. We have one week more to wait and see what happens in the last 10 days.
“I think this is my sixth season and the most unsettled group we are working with. That is why we are relaxed and calm. Some situations we cannot fix. Nothing to say about that, situations that are going on in the squad. Still we need to wait.
“That is the circumstances after playing the Champions League (final) on June 1, we knew that some situations like this would happen but for us and the club it’s difficult to handle. What can we do? We can only wait.
“I cannot do more than try to help the team find the best dynamic to train and not to create too many problems and be a person who is not being very emphatic, but understand every single situation and try to get a good result.”
Pochettino was evasive when asked whether Eriksen was left on the bench because his departure is imminent.
“I don’t know. I don’t know. Why you ask me? Maybe you know something,” he said. “It’s so difficult, the situation. We cannot blame one party or another. That is the situation, the circumstances.
“We arrive today with different players and different situations in the squad but I don’t want to justify our performance because of that. I want to make clear the point.
“When you play football and are on the pitch, you don’t think about these situations.”
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