Question

Find the value of a and b if (√7-2) / (√7+2) = a√7+b​

Answer 1

Answer:

a=-4/5,b=11/5

Step-by-step explanation:

(√7-2)/(√7+2)=a√7+b

Rationalise the denominator by multiplying (√7-2) to numerator and denominator

(√7-2)(√7-2)/(√7+2)(√7-2)=(√7-2)^2/(7-4)

=(7+4-4√7)/5

=(11-4√7)/5

compare a√7+b=(11/5-4√7/5)

Therefore,a=-4/5,b=11/5

Answer 2

$\huge \sf \color{red}\underline{Answer :}$

$\large \color{blue}\boxed{ b= \frac{11}{3}} , \boxed{a=-\frac{4}{3}√7}$

$\huge \sf \color{red}\underline{Solution :}$

$\large\frac{√7-2}{√7+2}×\frac{√7-2}{√7+2}\\\\ \large = > \frac{7+4+4√7}{7-4}\\ \\ \large = > \frac{11+4√7}{3} \\ \\ \large = > \frac{11}{3} +\frac{4√7}{3}$

$\color{green}━━━━━━━━━━━━━━━━━━━━━━━━━$

Hence,

$\sf \large \bf \color{blue} b=\frac{11}{3} \ , \ a= -\frac{4}{3}√7$

$\color{green}━━━━━━━━━━━━━━━━━━━━━━━━━$