Question
If $x=\frac{2}{3+\sqrt7},$ then $(x - 3)^2=$
✓
Answer
$\text{x}=\frac{2}{3+\sqrt7}=\frac{2}{3+\sqrt7}\times\frac{3-\sqrt7}{3-\sqrt7}=\frac{2(3-\sqrt7)}{3-\sqrt7}$
$\ =\frac{6-2\sqrt7}{9-7}=\frac{6-2\sqrt7}{2}=3-2\sqrt7$
Now $(\text{x}-3)^2=(\not3-\sqrt7-\not3)^2=\big(-\sqrt7\big)^2=7$
$\ =\frac{6-2\sqrt7}{9-7}=\frac{6-2\sqrt7}{2}=3-2\sqrt7$
Now $(\text{x}-3)^2=(\not3-\sqrt7-\not3)^2=\big(-\sqrt7\big)^2=7$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
→→→→→
The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. The smallest of these angles is:
- 45°
- 60°
- 36°
- 48°
A cube of side $4\ cm$ contains a sphere touching its sides. Find the approximate volume of the gap in between.
→The factors of $x^3 - 1 + y^3 + 3xy$ are:
→In a $\triangle\text{ABC},$ if $\angle\text{B} = \angle\text{C} = 45^\circ,$ which is the longest side?
→The equation of a line parallel to x-axis and 3 units above the origin is:
If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is:
The mean of 100 items was found to be 64. Later on it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. The correct mean is:
Which of the following is a polynomial?
→- $\sqrt[3]{\text{y}}+4$
- $\sqrt{\text{y}}-3$
- $\text{y}$
- $\frac{1}{\sqrt{\text{y}}}+7$
Write the correct answer in the following:
D and E are the mid-points of the sides AB and AC respectively of $\Delta\text{ABC}.$ DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is:
→D and E are the mid-points of the sides AB and AC respectively of $\Delta\text{ABC}.$ DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is: