Question

if a + b + c equal to -1 and a b + BC + CA is equal to minus 4 then find the value of a square + b square + c square

Answer 1

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

GIVEN:

→$a+b+c=-1$

→$ab + bc+ca =-4$

TO FIND:

♠$The \:value \:of\: a^{2}+b^{2}+c^{2}$

SOLUTION:

WE HAVE,

=>$a+b+c=-1$

On squaring both sides, we have;

=>$(a+b+c) ^{2}=(-1)^{2}$

=>$(a+b+c)^{2}=-1$

=>$a^{2}+b^{2}+c^{2}+2(ab+bc+ca)=1$

$\large\green{\boxed{(x+y+z)^{2}=x^{2}+y^{2}+z^{2}+2(xy+yz+xz)}}$

=>$a^{2}+b^{2}+c^{2}+2(-4)=1$

(given)

=>$a^{2}+b^{2}+c^{2}-8 =1$

=>$a^{2}+b^{2}+c^{2} =(1+8)$

=>$a^{2}+b^{2}+c^{2} =9$

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Hence,$a^{2}+b^{2}+c^{2}=9$

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$\huge\orange{\boxed{Answer=9}}$