Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If $x^2+4 y^2=53$ and $x-2 y=5$, then what is the value of $x^3-8 y^3$ ?

Options:

155

335

-85

85

Correct Answer:

335

Explanation:

If $x^2+4 y^2=53$ and $x-2 y=5$,

What is the value of $x^3-8 y^3$ 

( a - b )2 = a2 + b2 - 2×2ab

(5 )2 = 53 - 4ab

4ab = 28

ab = 7

If x - y  = n

then, $x^3 - y^3$ = n3 + 3 × n × xy

$x^3-8 y^3$   = 53 + 3 × 5 × 2 × 7

$x^3-8 y^3$  = 125 + 210

$x^3-8 y^3$   = 335