Test Index

RRB ALP CBT I 16 Feb 2026 Shift 2 Paper

© examsnet.com

Question : 31 of 75

Marks: +1, -0

If

2x + 3y = 11

xy = 2

, find the value of

4x^{2} + 9y^{2}

.

97
117
101
109

Solution:

Concept:

Use the algebraic identity

(a+b)^2 = a^2 + b^2 + 2ab

to connect the given sum and product.

Explanation:

Given

2x + 3y = 11

and

xy = 2

.

We need

4x^2 + 9y^2

, which equals

(2x)^2 + (3y)^2

.

Square both sides of

2x + 3y = 11

:

(2x + 3y)^2 = 11^2

(2x)^2 + (3y)^2 + 2(2x)(3y) = 121

4x^2 + 9y^2 + 12xy = 121

Substitute

xy = 2

:

4x^2 + 9y^2 + 12(2) = 121

4x^2 + 9y^2 + 24 = 121

4x^2 + 9y^2 = 121 - 24 = 97

Answer:

4x^2 + 9y^2 = 97

, so the correct option is A.

© examsnet.com

Go to Question:

Prev Question

Next Question