If a+b=7 and a b=12, find the value of a^2+b^2 - Vidyadip

Question

If $a+b=7$ and $a b=12$, find the value of $a^2+b^2$

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Answer

We have to find the value of $a^2+b^2$
Given $\mathrm{a}+\mathrm{b}=7, \mathrm{ab}=12$
Using identity $(a+b)^2=a^2+2 a b+b^2$
By substituting the value of $a+b=7, a b=12$ we get
$(a+b)^2=a^2+b^2+2 \times a b$
$(7)^2=a^2+b^2+2 \times 12$
$49=a^2+b^2+24$
By transposing $+24$ to left hand side we get,
$49-24=a^2+b^2$
$25=a^2+b^2$
Hence the value of $a^2+b^2$ is $25$ .

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