CAT 2015 Quantitative Ability

Question : 1 of 34

Marks: +1, -0

x^4 - y^4 = 15,

where x and y are natural numbers, then find the value of the expression

x^4 + y^4.

Solution:

(x^2 - y^2)(x^2 + y^2) = 15

⇒(x^2 - y^2)(x^2 + y^2) = 1×15 = 3×5

⇒ x^2 - y^2 = 3\;\text"and"\; x^2 + y^2 = 5

(because x and y are natural numbers)

∴\;\;2x^2 = 8

⇒\; x^2 = 4

∴\;\;y^2 = 1

⇒ x^4 + y^4 =4^2 + 1^2 = 17

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