Question

if a²+ b² + c² =77 and a+b+c=15, then
find the value of ab+ +bc+ca​

Answer 1

$\large{\bf{\underline{\blue{ANSWER}}}}$

$\large{\bf{\underline{\red{GIVEN}}}}$

$a^2+b^2+c^2=77$

$a+b+c=15$

$\large{\bf{\underline{\pink{TO\:FIND}}}}$

$ab+bc+ca$

$\text\tt{USING IDENTITY (a+b+c)^2}$

$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$

Now Put the given values.

$15^2=77+2(ab+bc+ca)$

$225-77=2(ab+bc+ca)$

$148=2(ab+bc+ca)$

$ab+bc+ca=74$

Some of The useful identities.

$\bf\blue{(a+b)^2=a^2+b^2+2ab}$

$\bf\red{(a-b)^2=a^2-2ab+b^2}$