Question

a-b=13,a*b=10finda^2+b^2=?​

Answer 1

Step-by-step explanation:

By using the identity

(a-b)^2 = a^2 + b^2 - 2ab

Substituting the values as

(13)^2 = a^2 + b^2 - 2(10)

So let a^2 + b^2 be x

169 = x - 20

169 + 20 = x

189 = x

Answer 2

$\huge \bf{Answer} \\ \ {a}^{2} + {b}^{2} = 189 \\ \\ \star \: fotmula \: used \: \\ \implies {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ \huge \red{ \bf{Explanation}} \\ \\ A.T.Q. \\ (a - b) = 13 \: \: \: \: ab = 10 \\ \\ using \: formula \\ \\ \implies \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ \implies \: ({a}^{2} + {b}^{2} ) = {(a - b)}^{2} + 2ab \\ \\ substitute \: the \: given \: values \\ \\ \implies \: ( {a}^{2} + {b}^{2} ) = {(13)}^{2} + 2 \times 10 \\ \\ \implies \: ( {a}^{2} + {b}^{2} ) = 169 + 20 \\ \\ \implies \: \red{ \boxed{( {a}^{2} + {b}^{2} ) = 189}} \: \: \\ \\ \: this \: is \: the \: required \: answer.$