Question

1/(3-√8)-1/(√8-√7)+1/(√7-√6)-1/(√6-√5)+1/(√7-6)=5​

Answer 1

$\textbf{\huge\underline{\red{Solution:-}} }$

1(/3-√8)×(3+√8)/(3+√8)-1/(√8-√7)×(√8+√7)/(√8+√7)+1/(√7-√6)×(√7+√6)/(√7+√6)-1/(√6-√5)×(√6+√5)/(√6+√5)+1/(√5-2)×(√5+2)/(√5+2)

$\implies$(3+√8)/(3)²-(√8)²-(√8+√7)/(√8)²-(√7)²+(√7+√6)/(√7)²-(√6)²-(√6+√5)/(√6)²-(√5)²+(√5+2)/(√5)²-(2)²

$\implies$(3+√8)/1-(√8+√7)/1+(√7+√6)/1-(√6+√5)/1+(√5+2)/1

3+√8-√8-√7+√7+√6-√6-√5+√5+2

$\implies$3+2

$\implies$5

$\small\underline\bold\red{Hence\:Proved}$

Answer 2

5

1(/3-√8)*(3+√8)/(3+√8)-1/(√8-√7)*(√8+√7)/(√8+√7)+1/(√7-√6)*(√7+√6)/(√7+√6)-1/(√6-√5)*(√6+√5)/(√6+√5)+1/(√5-2)*(√5+2)/(√5+2)

(3+√8)/(3)²-(√8)²-(√8+√7)/(√8)²-(√7)²+(√7+√6)/(√7)²-(√6)²-(√6+√5)/(√6)²-(√5)²+(√5+2)/(√5)²-(2)²

(3+√8)/1-(√8+√7)/1+(√7+√6)/1-(√6+√5)/1+(√5+2)/1

3+√8-√8-√7+√7+√6-√6-√5+√5+2

3+2

=5