Question

if a= root5/8 and 8/a =b root 5 the find the value of b​

Answer 1

Answer:

You multiply the numerator and the denominator by the “conjugate” of  7−5–√ , that is  7+5–√ :

7+5√7−5√=(7+5√)2(7−5√)(7+5√) .

Then you use the remarkable identities:

(x+y)2=x2+y2+2xy  

(x+y)(x−y)=x2−y2  

So that you obtain:

(7+5–√)2=49+5+145–√=54+145–√  

(7−5–√)(7+5–√)=49−5=44  

Thus, the expression  7+5√7−5√ is equal to:

54+145√44=2722+7225–√  

The solution is then  a=2722 , and  b=722 .

Step-by-step explanation: