Question

If a+b+c=22 and ab+bc+ca =54 then a square + b square + c square =​

Answer 1

Answer:

376

Step-by-step explanation:

a² + b² + c² = (a + b + c)² - 2(ab + bc + ca)

= 22² - 2(54)

= 484 - 108

= 376

Answer 2

Given,

• a + b + c = 22

• ab + bc + ca = 54

We know,

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

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

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

Applying the values to the equation:

$\sf{\implies a^2+b^2+c^2= (22)^2-(2\times54)}$

$\sf{\implies a^2+b^2+c^2=484-108}$

$\sf{\implies a^2+b^2+c^2=376}$

$\boxed{\sf{\therefore a^2+b^2+c^2=376}}$