Quadratic Surd

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #21

If `x = \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}` and `xy=1`, then show that, `\frac{x^2 - xy + y^2}{x^2 + xy + y^2} = 61/63`.

Question No: #22

If `x = \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}`, find the value of `\frac{2x^2-3x+2}{3x^2+2x+3}`.
Ans: `17/32`
SEE SOLUTION

Question No: #23

If `a = \sqrt{2}+1` and `b = \sqrt{2}-1`, then find the value of `\frac{1}{1+a} + \frac{1}{1+b}`

Question No: #24

If `x=\frac{1}{2-\sqrt{3}}` and `y=\frac{1}{2+\sqrt{3}}`, then find the value of `(\frac{1}{1+x} + \frac{1}{1+y})`.
Ans: `1`
SEE SOLUTION

Question No: #25

If `x = \sqrt{3}/2`, then find the value of `\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}`.
Ans: `\sqrt{3}`
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Question No: #26

If `x = \sqrt{3}/2`, then find the simplest value of `\frac{1+x}{1+\sqrt{1+x}} + \frac{1-x}{1-\sqrt{1-x}}`

Question No: #27

If `x = \sqrt{\frac{\sqrt{5}+1}{\sqrt{5}-1}}`, then find the value of `x^2-x`