Question

Choose the correct answer from the alternatives given.
If $a^2+b^2$ = 234 and ab = 108, then find the value of

$\frac{a+b}{a-b}$

• A. 10
• B. 8
• C. 5
• D. 4

Answer 1

The correct option is C 5

$\Rightarrow$ $a^2-b^2=234$ and $ab=108$

$\Rightarrow$ $(a+b{)}^2=a^2+b^2+2ab$

$=234+2\left(108\right)$

$=234+216$

$\therefore$ $(a+b{)}^2=450$ ----- ( 1 )

$\Rightarrow$ $(a-b{)}^2=a^2+b^2-2ab$

$=234-2\left(108\right)$

$=234-216$

$\therefore$ $(a-b{)}^2=18$ ----- ( 2 )

Now dividing ( 1 ) by ( 2 )

$\Rightarrow$ $\frac{(a+b{)}^2}{(a-b{)}^2}=\frac{450}{18}$

$\Rightarrow$ $\frac{(a+b{)}^2}{(a-b{)}^2}=25$

Now taking square root on both sides,

$\Rightarrow$ $\frac{a+b}{a-b}=5$