Question

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Answer 1

$\huge\sf\pink{Answer}$

☞ Your answer is 61

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$\huge\sf\blue{Given}$

✭ $\sf a+b=9$

✭ $\sf ab=10$

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$\huge\sf\gray{To \:Find}$

◈ Value of a²+b²?

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$\huge\sf\purple{Steps}$

☯ $\underline{\sf As \ Per \ the \ Question}$

➝ $\sf a+b=9\:\:\: -eq(1)$

Also given that,

➝ $\sf ab=10 \:\:\: -eq(2)$

So here I'll show you two methods,you may choose the one you feel is easy,

Method 1

Squaring both sides of eq(1)

➳ $\sf a+b=9$

➳ $\sf (a+b)^2=9^2$

➳ $\sf (a+b)^2 = 81$

We know that,

$\sf \underline{\boxed{\sf (a+b)^2 = a^2+2ab+b^2}}$

➳ $\sf a^2+2ab+b^2 = 81$

$\bigg\lgroup\sf Sub \ value \ of \ eq(2)\bigg\rgroup$

➳ $\sf a^2+2(10)+b^2=81$

➳ $\sf a^2+20+b^2=81$

➳ $\sf a^2+b^2 = 81-20$

➳ $\sf \orange{a^2+b^2 = 61}$

Method 2

»» $\sf a^2+b^2$

$\underline{\boxed{\sf a^2+b^2=(a+b)^2 - 2ab}}$

$\sf (a+b) = 9 \ and \ ab = 10$

»» $\sf (9)^2-2(10)$

»» $\sf 81-20$

»» $\sf \red{a^2+b^2 = 61}$

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