Question

If ab=4 and a-b=8,then find a^2+b^2​

Answer 1

Step-by-step explanation:

ab=4 a-b=8

a^2+b^2

=(a-b)^2+2ab

=(8)^2+2×4

=64+8

=72

Answer 2

$\underline{\boxed{\bold{Question}}}$  

↠ If (a × b) = 4 and (a - b) = 8 , then find a² + b²

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Algebraic identities are simple formulas that leads to easy calculation for problems related to algebraic operations.

$\underline{\boxed{\bold{Important\;Identities}}}$

$\red{:\implies (a+b)^{2} = a^{2} +2ab+b^{2} }$

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

$\red{:\implies a^{2} -b^{2} = (a-b)(a+b) }$

$\pink{:\implies (x+a)(x+b) = x^{2} +(a+b)x+ab }$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Given}}}$

↠  (a × b) = 4

↠ (a - b) = 8

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Answer}}}$

Let's Start !

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Let's solve this question by using 2nd identity.

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

$:\implies (8)^{2} = a^{2} -2(4)+b^{2}$

$:\implies 64 = a^{2} -8+b^{2}$

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

$\boxed{\bold{\blue{:\implies a^{2}+b^{2} = 72 }}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boxed{\boxed{\bold{\therefore a^{2}+b^{2} = 72 }}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Hope this helps u.../

【Brainly Advisor】