Question

solve this. and I want detailed explanation with shortcuts.. don't spams!!! otherwise I will report your answer!!!​

Answer 1

Answer:

x² + y² + z² = 26

Step-by-step explanation:

Given that x + y + z = 2, let's call this equation (1).

Square the equation (1) to obtain :

=> x² + y² + z² + 2(xy + yz + zx) = 4

Let's call x² + y² + z² = α

and xy + yz + zx = β

So,the equation (1) becomes :

α + 2β = 4..(2)

Now,also we are given that :

x³ + y³ + z³ -3xyz = 74

And you should probably be knowing factorisation? So,on factorising this given equation,we have :

(x+y+z) (x² + y² + z² - (xy + yz +zx)) = 74

Observe carefully,we the second bracket in LHS has both the terms that we assumed α and β,so just substitute that instead of those large disturbing terms. Also,we know that x+y+z = 2.

=> 2(α - β) = 74

=> 2α -2β = 74...(3)

Now, just eliminate β by adding equation (2) and (3),

=> α + 2β + 2α - 2β = 74 + 4

=> 3α = 78

=> α = 78/3

=> α = 26

And,we at the beginning assumed α = (x²+y²+z²),so the question is successfully killed.

Option (3) is correct.