Question

If l +m+n=8 and lm+mn+nl=15 then, evaluate l^2+m^2+n^2

Answer 1

$\mathcal{\green{\underline{\blue{GIVEN:}}}}$

• l + m + n = 8.
• lm + mn + nl = 15.

$\mathcal{\green{\underline{\blue{TO \:\: FIND:}}}}$

• l²+m²+n².

$\mathcal{\green{\underline{\blue{SOLUTION:}}}}$

There is a very interesting formula, which goes as :

$\boxed{\bold{\large{a^2+b^2+c^2=(a + b + c)^2 -2(ab+bc+ac)}}}$

This formula is popular, and is important too!

Using the above formula, we can  write l²+m²+n² as:

$\to \bf l^2+m^2+n^2=(l + m + n)^2 -2(lm+mn+ln)$

Substitute l + m + n = 8 and lm + mn + nl = 15.

$\to \bf l^2+m^2+n^2=(8)^2 -2(15)$

$\to \bf l^2+m^2+n^2=64 -30$

$\to \bf l^2+m^2+n^2=34$

$\huge\star\:\:{\orange{\underline{\pink{\mathbf{HOPE \:\: THIS \:\: HELPS \:\: :D}}}}}$