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Question

If (x+a)(x+b)=x25x300, find the values of a2+b2

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Solution

x25x300=x220x+15x300=x(x20)+15(x20)=(x20)(x+15)
Given (x+a)(x+b)=x25x300
Then (x+a)(x+b)=(x20)(x+15)
So, compare this we get a=20 and b=15
Then a2+b2=(20)2+(15)2=400+225=625

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