Question

√5x+3-√5x/√5x+3+√5x=3/7​

Answer 1

$\textbf{Given:}$

$\mathsf{\dfrac{\sqrt{5x+3}-\sqrt{5x}}{\sqrt{5x+3}+\sqrt{5x}}=\dfrac{3}{7}}$

$\textbf{To find:}$

$\textsf{Solution of the given equation}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{\sqrt{5x+3}-\sqrt{5x}}{\sqrt{5x+3}+\sqrt{5x}}=\dfrac{3}{7}}$

$\textsf{This can be written as}$

$\mathsf{7(\sqrt{5x+3}-\sqrt{5x})=3(\sqrt{5x+3}+\sqrt{5x})}$

$\mathsf{7\sqrt{5x+3}-7\sqrt{5x}=3\sqrt{5x+3}+3\sqrt{5x}}$

$\mathsf{7\sqrt{5x+3}-3\sqrt{5x+3}=3\sqrt{5x}+7\sqrt{5x}}$

$\mathsf{4\sqrt{5x+3}=10\sqrt{5x}}$

$\mathsf{2\sqrt{5x+3}=5\sqrt{5x}}$

$\textsf{Squaring on bothsides, we get}$

$\mathsf{4(5x+3)=25(5x)}$

$\mathsf{20x+12=125x}$

$\mathsf{12=105x}$

$\implies\mathsf{x=\dfrac{12}{105}}$

$\implies\boxed{\mathsf{x=\dfrac{4}{35}}}$

$\textbf{Find more:}$

Solve the simultaneous equations 3x –2y =5 and 2x + 5y = 16 by elimination by substitution.tell fast

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