Question

If x=√5-2/√5+2 and y=√5+2/√5-2 then show that x²-y²=-144√5

Answer 1

Hey....!!! here is ur answer.....☺️☺️☺️

Here...... Given that,

x = √5–2/√5+2

& y = √5+2/√5–2

then we have to prove that.......x²–y² = –144√5

On taking L.H.S.

x²–y² = (x+y)(x–y)
{As we know that ,a²–b²=(a+b)(a–b)}

=>{(√5–2/√5+2)+(√5+2/√5–2)}{(√5–2/√5+2)–(√5+2/√5–2)}

=>{(√5–2)(√5–2)+(√5+2)(√5+2)}/5-4×
{(√5–2)(√5–2)–(√5+2)(√5+2)}/5–4

=>(5+4–4√5+5+4+4√5)/1×
{5+4–4√5–(5+4+4√5)}/1

=>(18)×(–8√5)

=>–144√5 = R.H.S. Hence proved....

I hope it may help you........✌️✌️✌️