Question

If (a + b + c) = 5 and (ab + bc + ca = 10) then prove that ( a + + - 3abc = -25)


Answer karo!

Fastttttttttttt

- Utkarsh Pratham here!

Ex Proficient!​

Answer 1

$\large\sf\underline{\underline{\red{Correct \ Question}}}$

If a + b + c = 5 and ab+bc+ca= 10 then prove that a² + b² + c² - 3abc = -25

$\huge\sf\blue{Given}$

✭ a+b+c = 5

✭ ab+bc+ca = 10

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ a² + b² + c² - 3abc = -25

$\rule{110}1$

$\huge\sf\purple{Steps}$

Before Solving we should know the formula,

$\underline{\boxed{\sf (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca}}$

Substituting the given values,

➳ $\sf 5^2 = a^2+b^2+c^2+2(ab+bc+ca)$

➳ $\sf 25 = a^2+b^2+c^2+2(10)$

➳ $\sf 25 = a^2+b^2+c^2+20$

➳ $\sf 25-20 = a^2+b^2+c^2$

➳ $\sf 5 = a^2+b^2+c^2$

$\sf\bigg\lgroup (a+b+c)(a^2+b^2+c^2)-(ab+bc+ca)\bigg\rgroup$

➳ $\sf (5)(5-10)$

➳ $\sf \orange{-25}$

$\sf LHS = RHS$

$\sf Hence \ Proved!!$

$\rule{170}3$

Answer 2

Answer:

this is your answer

..

Step-by-step explanation:

...