If x2-11-2 -30- then x -A- -5-6- -5-6- 4 -30D- 22

The correct option is A √(5)+√(6) x^2 = 11 + 2√(30) x^2= 5 + 6 + 2(√(5))(√(6)) = (√(5))^2+(√(6))^2+2(√(5))(√(6)) =(√(5))^2+2(√(5))(√(6))+(√(6))^2 =(√(5)+ √(6)) ...

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Byju's Answer

Standard IX

Mathematics

Operations on Binomial Surds

If x2=11+2 √3...

Question

If $x^{2} = 11 + 2 \sqrt{30}$ , then $x$ = ______

$\sqrt{5} + \sqrt{6}$

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$\sqrt{5} - \sqrt{6}$

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$22$

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$4 \sqrt{30}$

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Solution

The correct option is A
$\sqrt{5} + \sqrt{6}$

$x^{2} = 11 + 2 \sqrt{30}$

$x^{2} = 5 + 6 + 2 (\sqrt{5}) (\sqrt{6})$

= $(\sqrt{5})^{2} + (\sqrt{6})^{2} + 2 (\sqrt{5}) (\sqrt{6})$

= $(\sqrt{5})^{2} + 2 (\sqrt{5}) (\sqrt{6}) + (\sqrt{6})^{2}$

= $(\sqrt{5} + \sqrt{6})^{2}$

$∴ x = \sqrt{5} + \sqrt{6}$

Hence (A)

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Similar questions

If $x = 5 - 2 \sqrt{6}$ , then $x + \frac{1}{x} =$ ___

If $x = \frac{\sqrt{5} - 2}{\sqrt{5} + 2}$ then $x^{2}$ = ___

The sum of $11 x^{2} - 8 x + 4$ and $6 x^{2} + 7 x - 10$ is:

Q. Question 4
The

11^{t h}

term of the AP

- 5, \frac{- 5}{2}, 0, \frac{5}{2}, \dots \dots

is

A) -20
B) 20
C) -30
D) 30

Q. Which of the following equations is quadratic ?
(1)

x^{2} + 2 x + 11 = 0

(2)

x^{2} - 2 x + 5 = x^{2}

(3)

{(x + 2)}^{2} = 2 x^{2}

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If x2=11+2√30, then x = ______

The correct option is A √5+√6 x2=11+2√30 x2=5+6+2(√5)(√6) = (√5)2+(√6)2+2(√5)(√6) =(√5)2+2(√5)(√6)+(√6)2 =(√5+√6)2 ∴x=√5+√6 Hence (A)

If $x^{2} = 11 + 2 \sqrt{30}$ , then $x$ = ______