MATHEMATICS

JAMB 2008 - Question 9

Mathematics 2008 JAMB Past Questions - Question 9: if 1+√2/ 1-√2 is expressed in the form x+y√ 2,find the value of x and y.

if 1+√2/ 1-√2 is expressed in the form x+y√ 2,find the value of x and y.
A:
B:
C:
D:
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Correct Answer

A

Explanation

To express the fraction (1 + √2) / (1 - √2) in the form x + y√2, we can use the conjugate of the denominator to rationalize the expression.Multiplying the numerator and denominator by the conjugate of the denominator, which is (1 + √2), we get:[(1 + √2) / (1 - √2)] * [(1 + √2) / (1 + √2)]Expanding the numerator and denominator, we have:[(1 + √2)(1 + √2)] / [(1 - √2)(1 + √2)]Simplifying further:[1 + 2√2 + (√2)^2] / [1 - (√2)^2][1 + 2√2 + 2] / [1 - 2][3 + 2√2] / [-1]Now, we can separate the fraction into two parts:x = 3 / -1 = -3y = 2 / -1 = -2Therefore, the value of x is -3 and the value of y is -2.