Question

if a =✓5+1÷✓5-1 and b=✓5-1÷✓5+1,find the value of (✓a+✓b)^2​

Answer 1

a=

√5+1/√5-1×√5+1/√5+1

(√5+1)^2/√5^2-1^2=5+1+2√5/5-1=6+2√5/4=3+√5/2

b=

√5-1/√5+1×√5-1/√5-1=5+1-2√5/5-1=6-2√5/4=3-√5/2

:.

(a+b)^2=(3/2+√5/2+3/2-√5/2)

=(3/2+3/2)^2=9/4+9/4+2×3/2×3/2=18/4+81