Question

If ab=4 and a-b=8,then find a^2+b^2​

Answer 1

$\huge\fbox\pink{A}\fbox\blue{n}\fbox\purple{S}\fbox\green{w}\fbox\red{E}\fbox\orange{r}$

$\Large{\blue{\tt{\underline{\underline{Given \ :-}}}}}$

${\sf{☞ \ ab \ = \ 4}}$

${\sf{☞ \ a² + b² \ = \ 8}}$

$\Large{\orange{\tt{\underline{\underline{To \ find \ :-}}}}}$

${\sf{↣ \ a²+b² \ }}$

$\Large{\green{\tt{\underline{\underline{Solution \ :-}}}}}$

${\large{\bf{As \ we \ know \ that}}}$

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

${\large{\bf{or}}}$

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

${\Large{\sf{Substituting \ the \ values }}}$

${\sf{↣ {a}^{2} + {b}^{2} = \: {(a - b)}^{2} + 2ab }}$

${\sf{↣{a}^{2} + {b}^{2} \: = \: {8}^{2} \: + \: 2 \times 4}}$

${\sf{↣{a}^{2} + {b}^{2} \: = \: 64 \: + \: 8}}$

${\sf{↣{a}^{2} + {b}^{2} \: = \: 72}}$

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