Simplification And Evaluation | MCQs

Explanation

Given:

ab + bc + ca = -4

a² + b² + c² = 17

Using the identity (a + b + c)² = a² + b² + c² + 2(ab + bc + ca):

(a + b + c)² = 17 + 2(-4)

= 17 - 8

= 9

a + b + c = ±√9

= ±3

Explanation

Given log(x) - 2log(y):

Using logarithmic properties:

log(x) - 2log(y) = log(x) - log(y^2) = log(x/y^2)

Explanation

Given w⁻¹³ = w², let's assume a cyclic pattern:

If w¹⁵ = 1, then w⁻¹³ = w² fits the pattern w⁻¹³ = w^(15-13) = w².