Question

7+√2/7-√2=a+b√2
value of a and b by rationalize method
​

Answer 1

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

$\large \color{blue}\boxed{ a= \frac{51}{47}} , \boxed{b=\frac{14}{47}√2}$

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

$\large\frac{7+√2}{7-√2}×\frac{7+√2}{7+√2}\\\\ \large => \frac{49+2+14√2}{49-2}\\ \\ \large => \frac{51+14√2}{47} \\ \\ \large => \frac{51}{47} +\frac{14√2}{47}$

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

Hence,

$\sf \large \bf \color{blue} a=\frac{51}{47} \ , \ b=\frac{14}{47}√2$

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

Answer 2

$\huge\sf\color{red}\underline{Question}$

$7+\dfrac{√2}{7}-√2=a+b√2$

${\large{\underline{\underline{\bf{Answer}}}}}$

a=$\dfrac{51}{47}$

b=$\dfrac{14}{47}√2$

${\large{\underline{\underline{\bf{Solution}}}}}$

$\dfrac{7+√2}{7-√2}$$\dfrac{7+√2}{7+√2}$

=> $\dfrac{49+2+14√2}{49-2}$

=> $\dfrac{51}{47}+{14√2}{47}$

=>a=$\dfrac{51}{47}$, b=$\dfrac{14}{47}√2$