If (a³ + b³) is proportional to (a² – b²), then (a² - ab + b²) is proportional to

Question

Question

This question was previously asked in

CDS 02/2022 Elementary Mathematics Official Paper (Held On 04 Sep 2022)

Answer 1

Formula used:

a3 + b3 = (a + b)(a2 - ab + b2)

a² - b²= (a + b)(a - b)

Calculation:

According to the question

(a3 + b3) ∝ (a2 – b2)

Using the above identities

⇒ (a + b)(a 2 - ab + b2) ∝ (a + b)(a - b)

⇒ (a 2 - ab + b2) ∝ (a - b)

∴ (a 2 - ab + b2) will be proportional to the a - b