Question

if a + b = -c then prove that a cube + b cube + c cube =3 abc​

Answer 1

GIVEN:-

• a+b=-c

TO PROVE:-

• $a^3+b^3+c^3=3abc$

Now,

Using identity $\tt{a^3+b^3+c^3-3abc}$

$\tt{a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)}$

Now, Substituite the value of a+b.

$\tt{a^3+b^3+c^3-3abc=(-c+c)(a^2+b^2+c^2-ab-bc-ac)}$

$\tt{a^3+b^3+c^3-3abc=(0)(a^2+b^2+c^2-ab-bc-ac)}$

$\tt{a^3+b^3+c^3-3abc=0}$

$\tt{a^3+b^3+c^3=3abc}$

$\large\sf\blue{EXTRA\:INFORMATION}$

• $\tt{(a+b)^2=a^2+b^2+2ab}$

• $\tt{(a-b)^2=a^2-2ab+b^2}$

• $\tt{a^3+b^3=(a+b)(a^{2}-ab+b^{2})}$