Question

If (a + b) : (ab)^1/2 = 4:1, find the value of (a/b)1/2 + (b/a)^1/2.​

Answer 1

Step-by-step explanation:

a+bab√=41

=>aab√+bab√=4

=>ab−−√+ba−−√=4

Letab=x2

=>x2−−√+1x2√=4

=>x+1x=4

=>x2−4x+1=0

=>x=4±16–4(1)(1)√2=4±23√2=2±3–√

=>ab=x2=(2±3–√)2=4+3±43–√=7±43–√

a:b=7±43–√:1