If x=\frac{\sqrt3+1}{\sqrt3-1} and y=\frac{\sqrt3-1}{\sqrt3+1} then the value of x^2/y+y^2/x is:

Powers and Roots Practice Test 4

Question : 18 of 40

Marks: +1, -0

x={√3+1}/{√3-1}

and

y={√3-1}/{√3+1}

then the value of

x^2/y+y^2/x

is:

Solution:

x={√3+1}/{√3-1}×{√3+1}/{√3+1}=2+√3

Similarly, the value of

y={√3-1}/{√3+1}

2-√3

Value of

x^2/y+y^2/x={x^3+y^3}/{xy}

={ (2+√3)^3+ (2-√3)^3}/{(2+√3)(2-√3)}

={ (2+√3)^3+ (2-√3)^3}/{1}

(a+b)^3=a^3+b^3+3ab(a+b)

(a-b)^3=a^3-b^3-3ab(a-b)

∴2^3+(√3)^3+3×2×√3(2+√3)+2^3-(√3)^3-3×2√3(2-√3)

=8+3√3+6√3(2+√3)+8-3√3-6√3(2-√3)

=8+3√3+12√3+18+8-3√3-12√3+18

=8+18+8+18=52

Go to Question:

Prev Question

Next Question