Question

If a = √10+ √ 5 ÷ √ 10 -√5 and b= √10-√ 5÷ √10 +√5 ; then show that √a-√ b- 2√ ab= 0answer this question ✔✔BE BRAINLY ❣

Answer 1

Answer:

given a=( √10 +√5 )÷ ( √10 -√5)  

         b=(√10 - √5 )÷ ( √10 + √5 )

 multiplying the conjugate on the numerator and the denominator

so a= $\frac{\sqrt{10} +\sqrt{5} }{\sqrt{10 } -\sqrt{5} }$  ×$\frac{\sqrt{10} +\sqrt{5} }{\sqrt{10} +\sqrt{5}}$

      = (10 +2√50 + 5 ) ÷ ( 10-5)

      = (15 +2√50 ) ÷5

      = 3 +2√2

 b = ( √10 -√5) (√10 - √5 ) ÷ (√10 +√5 )(√10 - √5 )

  = (10 -2√50+5 )÷ (10 -5)

  = (15 -2√50)/ 5

  =3-2√2

ab ={ ( √10 +√5 )÷ ( √10 -√5) } ×{(√10 - √5 )÷ ( √10 + √5 )}

    = 1

LHS = √a-√ b- 2√ ab

      = √(3 +2√2) -√(3-2√2)  - 2√1

       = 2 -2

      = 0 =RHS

HENCE PROVED