Question

if ab+bc+ca=90 find the value of a2 +b2+c2

Answer 1

$\large\mathtt\red{Heyy~!!~below~is~your~ans.}$

$\huge\mathtt\red{QUESTION-}$

$\large{\sf{If~ab+bc+ca=90~then~what~is~value~}}$

$\large{\sf{of~a²+b²+c²}}$

$\huge\mathtt\blue{SOLUTION}$

$\large\green{\sf{Given-}}$

$\large{\sf{ab+bc+ca=90}}$

$\large{\sf{abc=20}}$

$\large\purple{\sf{To~find-}}$

$\large{\sf{a²+b²+c²}}$

$\large\pink{\sf{Solution-}}$

$\large{\sf{Using~identity~÷}}$

$\large{\sf{(a+b+c)²~=a²+b²+c²+2ab+2ca+2ca}}$

$\large{\sf{Hence~we~have-}}$

$\large{\sf{(a+b+c)²=a²+b²+c²+2(ab+bc+ca)}}$

$\large{\sf{(20)²=a²+b²+c²+2(90)}}$

$\large{\sf{400=a²+b²+c²+180}}$

$\large{\sf{a²+b²+c²=400-180}}$

$\large{\sf{a²+b²+c²=220}}$

$\large\mathtt\blue{.°.~Value~of~a²+b²+c²=220}$

$\green{✤✤-Hope~it~helps-✤✤}$