Math, asked by abhi199, 1 year ago

√7 - 2/√7 + 2 = a√7 + b

Answers

Answered by MaheswariS
71

\textbf{Given:}

\dfrac{\sqrt{7}-2}{\sqrt{7}+2}=a\,\sqrt{7}+b

\textbf{To find:}

\text{The values of a and b}

\textbf{Solution:}

\text{Consider,}

\dfrac{\sqrt{7}-2}{\sqrt{7}+2}=a\,\sqrt{7}+b

\text{To rationalize the denominator, multiply}

\text{both numerator and denominator by $\sqrt{7}-2$}

\dfrac{\sqrt{7}-2}{\sqrt{7}+2}{\times}\dfrac{\sqrt{7}-2}{\sqrt{7}-2}=a\,\sqrt{7}+b

\dfrac{(\sqrt{7}-2)^2}{(\sqrt{7})^2-2^2}=a\,\sqrt{7}+b

\dfrac{7+4-4\sqrt{7}}{7-4}=a\,\sqrt{7}+b

\dfrac{11-4\sqrt{7}}{3}=a\,\sqrt{7}+b

\dfrac{11}{3}-\dfrac{4}{3}\sqrt{7}=a\,\sqrt{7}+b

-\dfrac{4}{3}\sqrt{7}+\dfrac{11}{3}=a\,\sqrt{7}+b

\text{Comparing on bothsides, we get}

a=\dfrac{-4}{3} \text{and}

b=\dfrac{11}{3}

\therefore\textbf{The values of a and b are $\bf\dfrac{-4}{3}$ and $\bf\dfrac{11}{3}$}

Find more:

If p and q are rational numbers and

p√15q ? 2√3 -√5/4√3-3√5 find the value of p and q

https://brainly.in/question/16694887

Answered by famia
7

Step-by-step explanation:

-4/3√7+11/3

is the ans

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