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Question

If x and y are rational numbers such that 2+323=x+y3, find the value of x and y.

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Solution

We have,
2+323=x+y3

On rationalizing the denominator, we get:
2+323×2+32+3=x+y3

(2+3)222(3)2=x+y3

4+3+4343=x+y3

7+43=x+y3

On comparing both sides, we get:
x=7,y=4

Hence, the values of x and y are 7 and 4, respectively.

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