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Mashcka [7]
2 years ago
11

If ab = 8 and a^2+b^2=16, then what is the value of (a+b)^2?

Mathematics
1 answer:
aksik [14]2 years ago
6 0

ab = 8 & a^{2} + b^{2} = 16 so , ( a+b )^{2} = 32 .

<u>Step-by-step explanation:</u>

Here we have , ab= 8 & a^2+b^2=16 i.e. ab = 8  and a^{2} + b^{2} = 16 .

We need to find value of (a+b)^2 i.e. (a+b)^{2} :

It's and identity and we know that ( a+b )^{2} = a^{2} +b^{2} +2ab

⇒ ( a+b )^{2} = a^{2} +b^{2} +2ab

⇒ ( a+b )^{2} = (a^{2} +b^{2}) +2(ab)

⇒ ( a+b )^{2} = (16) +2(8)

⇒ ( a+b )^{2} = (16) +(16)

⇒ ( a+b )^{2} = 32

∴ ab = 8 & a^{2} + b^{2} = 16 so , ( a+b )^{2} = 32 .

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