If frac{sqrt{5+x}+sqrt{5-x}}{sqrt{5+x}-sqrt{5 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given the equation: $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$Applying the Componendo and Dividendo rule,which states that if $\frac{

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(D) Given the equation: $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$Applying the Componendo and Dividendo rule,which states that if $\frac{a}{b} = \frac{c}{d}$,then $\frac{a+b}{a-b} = \frac{c+d}{c-d}$:Let $a = \sqrt{5+x}+\sqrt{5-x}$ and $b = \sqrt{5+x}-\sqrt{5-x}$.Then $\frac{(\sqrt{5+x}+\sqrt{5-x}) + (\sqrt{5+x}-\sqrt{5-x})}{(\sqrt{5+x}+\sqrt{5-x}) - (\sqrt{5+x}-\sqrt{5-x})} = \frac{3+1}{3-1}$Simplifying the numerator and denominator:$\frac{2\sqrt{5+x}}{2\sqrt{5-x}} = \frac{4}{2}$$\frac{\sqrt{5+x}}{\sqrt{5-x}} = 2$Squaring both sides:$\frac{5+x}{5-x} = 4$$5+x = 4(5-x)$$5+x = 20 - 4x$$5x = 15$$x = 3$Thus,the value of $x$ is $3$.

If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3,$ then what is the value of $x?$

Similar Questions

If $x - (1/x) = \sqrt{13}$,then what is the value of $x^5 - (1/x^5)$?

What approximate value will come in place of the question mark $(?)$ in the given equation? (You are not expected to calculate the exact value)
$2775 \times \frac{160}{\sqrt{?}} = 5550$

Which of the following fractions are written in ascending order?

If the square of the sum of three positive consecutive natural numbers exceeds the sum of their squares by $292$,then what is the largest of the three numbers?

Simplify: $1-[2-\{5-(4-3-2)\}]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module