Question

If x=√5+2, then find the value of x ​

Answer 1

GIVEN:

$\\ \\ \\ x = \sqrt{5 } + 2$

TO FIND:

$\\ \\ \\ {x}^{2} + \frac{1}{ {x}^{2} }$

SOLUTION:

$\\ \\ \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{5} + 2 } \\ \\ \\ \\ = \frac{( \sqrt{5} - 2) }{{( \sqrt{5} + 2)( \sqrt{5} - 2)} } \\ \\ \\ \\ = \frac{ \sqrt{5} - 2}{( \sqrt{ {5})^{2} } - {(2)}^{2} } \\ \\ \\ \\ = \frac{( \sqrt{5} - 2)}{5 - 4} \\ \\ \\ = \sqrt{5} - 2 \: - - - (answer) \\ \\ \\ \\ x + \frac{1}{x} = \sqrt{5} + 2 + \sqrt{5} - 2 \\ \\ \\ = 2 \sqrt{5} \\ \\ \\ \\ {(x + \frac{1}{x} )}^{2} = {(2 \sqrt{5}) }^{2} = 20 \: \: \: (answer)$

Answer 2

Answer:

The base and height of a triangle are in the ratio 4:3. If the base is increased by 4 cm and the height is decreased by 2 cm, the area of the triangle remains the same. Find the base and the heightThe base and height of a triangle are in the ratio 4:3. If the base is increased by 4 cm and the height is decreased by 2 cm, the area of the triangle remains the same. Find the base and the heightThe base and height of a triangle are in the ratio 4:3. If the base is increased by 4 cm and the height is decreased by 2 cm, the area of the triangle remains the same. Find the base and the height