If x=2 3+ 7 , then (x - 3)^2 = - Vidyadip

MCQ

If $\text{x}=\frac{2}{3+\sqrt7},$ then $(x - 3)^2 =$

A
$1$
B
$3$
C
$6$
✓
$7$

✓

Answer

Correct option: D.

$7$

$\text{x}=\frac{2}{3+\sqrt7}=\frac{2}{3+\sqrt7}\times\frac{3-\sqrt7}{3-\sqrt7}=\frac{2(3-\sqrt7)}{3-\sqrt7}\\ \ =\frac{6-2\sqrt7}{9-7}=\frac{6-2\sqrt7}{2}=3-2\sqrt7$
Now $(\text{x}-3)^2=(\not3-\sqrt7-\not3)^2=\big(-\sqrt7\big)^2=7$
Hence, correct option is $(d).$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ(1M)" from Rationalisation→Rationalisation — all question types→Maths STD 9 question papers→Maharashtra Board STD 9 question papers→Maharashtra Board question paper generator→

Similar questions

Radius of a circle is $10$ cm and distance of a chord from the centre is $6$ cm. Hence, the length of the chord is ____.

Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is:

In a triangle, an exterior angle at a vertex is $95^\circ$ and its one of the interior opposite angle is $55^\circ ,$ then the measure of the other interior angle is:

Euclid stated that 'all right angles are equal to each other', in the form of:

In a sphere the number of faces is:

If $V$ is the volume of a cuboid of Dimensions $x, y, z$ and $A$ is its surface area, then $\frac{\text{A}}{\text{V}}$

If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is:

In $\triangle\text{ABC, BC = AB}$ and $\angle\text{B}=80^{\circ}.$ Then, $\angle\text{A = ?}$

The perpendicular distance of the point $P(4, 3)$ from $x-$ axis is:

$\left(4 x^2+4 x-3\right)=?$