Question

a+b=25 and ab=25 find the value of a-b

Answer 1

( a + b ) =25

On squaring both sides, we get



( a + b )^2 = 25^2

${a}^{2} + {b}^{2} + 2ab \: = 625 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: | \: \bold{ \: {(a + b)}^{2} = {a }^{2} + {b}^{2} + 2ab}$



$\bold{ \underline{ value \: of \: ab \: is \: given \: and \: it \: is \: 25}}$

So,



=> a² + b² + 2( 25 ) = 625

=> a² + b² + 50 = 625

=> a² + b² = 575




Now, add - 2ab on both sides,



${a}^{2} + {b}^{2} - 2ab \: = 575 - 2ab \\ \\ \\ {(a - b)}^{2} = 575 - 2(25) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \: {a}^{2} + {b}^{2} - 2ab = {(a - b)}^{2} }$

( a - b )² = 575 - 50

( a - b )² = 525

a - b = √525

a - b = 5√21