Question

(√5+1)/(√5-1)×(√5+1)/(√5+1)​

Answer 1

$\huge\underline\mathrm\purple{Solution}$

(√5+1)(√5-1)×(√5+1)(√5+1)

(√5)²-(1)²×(√5+1)²

5-1×[(√5)²+(1)²+2×√5×1]

4[5+1+2√5]

4[6+2√5]

24+8√5

$\bold\blue{NOTE}$

• (a-b)(a+b) = a²-b²
• (a+b)² = a²+b²+2ab

[all are used in solving this question]

Answer 2

$\huge\underline\mathcal\orange{Question}$

(√5+1)/(√5-1)×(√5+1)/(√5+1)

$\huge\underline\mathcal\orange{Solution}$

(√5+1)/(√5-1)×(√5+1)/(√5+1)

Applying both identity a²-b²= (a+b)(a-b) &

(a+b)² = a²+b²+2ab

= (√5)²-(1)²×[(√5+1)²]

= 5-1[(√5)²+(1)²+2×√5×1]

= 4[5+1+2√5]

= 4[6+2√5]

= 24 + 8√5