Question

if a + b + c is equals to 9 and AB + BC + CA is equals to 40, show that a square + b square + c square is equals to 1 ​

Answer 1

$\huge\red{\mathfrak{ Answer }}$

a+b+c= 9

ab+bc+ca= 40

To show

a^2+b^2+c^2= 1

LHS = a^2+b^2+c^2= (a+b+c)^2-(2(ab+bc+ca)= (9)^2-2(40)= 81-80= 1

RHS= 1

LHS =RHS

hope it helps ✌

Answer 2

a²+b²+c²=(a+b+c)²-2ab-2bc-2ac=9²-40×2=1

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