Question

If a+b=15 and ab=56,find the value of (a^2+b^2)

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{a^{2}+b^{2}=113}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies a + b = 15 \\ \\ \tt : \implies ab = 56 \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies {a}^{2} + {b }^{2} = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab \\ \\ \text{Putting \: given \: values} \\ \\ \tt: \implies {a}^{2} + {b}^{2} = {15}^{2} - 2 \times 56 \\ \\ \tt: \implies {a}^{2} + {b}^{2} = 225 - 112 \\ \\ \green{\tt: \implies {a}^{2} + {b}^{2} = 113} \\ \\ \blue{\bold{Some \: related \: formula}} \\ \blue{\tt \circ \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab} \\ \\ \blue{\tt \circ \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab} \\ \\ \blue{\tt \circ \: {a}^{2} - {b}^{2} = (a + b)(a - b)} \\ \\ \blue{\tt \circ \: {a}^{2} + {b}^{2} = {(a - b)}^{2} - 2ab }$

Answer 2

$\tt{\huge{\green{Hello !!! }}}$

Question :

If a+b=15 and ab=56,find the value of (a^2+b^2).

Solution :

$\tt{\orange {Step-By-Step-Explaination \::- }}$

Identity Used :

$\tt{ \purple{ \leadsto{ {( a+ b)}^{2} = {a}^{2} + {b}^{2} + 2ab }}}$

Hence

$\tt{ \green{ \leadsto{ {a}^{2} + {b}^{2} = {(15)}^{2} - 112 = 113}}} ......(A)$

$\\ \\ \orange{\bold{Some \: related \: formula \: :-}} \\ \green{\tt \square \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab} \\ \\ \blue{\tt \square \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab} \\ \\ \red{\tt \square \: {a}^{2} - {b}^{2} = (a + b)(a - b)} \\ \\ \pink{\tt \square \: {a}^{2} + {b}^{2} = {(a - b)}^{2} - 2ab }$