Question

If (x + a) (x + b) (x + c) = x³ - 10 x² + 45 x - 15, then find the value a² + b² + c²

Answer 1

Answer:

Step-by-step explanation:

Here, we have to use the identity

(x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc

Comparing this with

x3 – 10x2 + 45x – 15 = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc

⇒ – 10 = a + b + c

Now, 1/a + 1/b + 1/c

=> (bc+ac+ab)/abc

=> -45/15

=> -3

And (ab + bc + ca) = 45

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

⇒ (– 10)2 – 2 × 45 = a2 + b2 + c2

⇒ 100 – 90 = a2 + b2 + c2

⇒ a2 + b2 + c2 = 10