Question

If a + b + c = 16 and ab + bc + ca = 40 then a² + b² + c² is equal to ______.

Options

• 136

• 156

• 176

• 196

Answer 1

If a + b + c = 16 and ab + bc + ca = 40 then a² + b² + c² is equal to 176.

Explanation:

We are given:

a + b + c = 16 

ab + bc + ca = 40

We need to find a² + b² + c².

Recall the identity:

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

Substitute the given values:

16² = a² + b² + c² + 2(40)

256 = a² + b² + c² + 80

So, a² + b² + c² = 256 – 80 = 176.