Question

if root 3 + root 2 by root 3 minus root 2 equal Mein a + b root 6 then the value of a and b is​

Answer 1

Answer:

a= root3 and b=1/3

Step-by-step explanation:

root3 +root2/root3 =a +b(root6)

root3 + root2×root3/root3×root3 =a +b(root6)

root3 +root6/3 = a+b(root6)

on comparing we will get

a=root3 and b= 1/3

Answer 2

Given :  (√3 + √2)/ (√3 - √2)   = a - b√6

To Find : Value of a & b

Solution:

(√3 + √2)/ (√3 - √2)    = a + b√6

(√3 + √2)/ (√3 - √2)

Rationalize the denominator

= (√3 + √2) (√3 + √2) /   (√3 -  √2) (√3 + √2)

Solving numerator

using (a + b)² = a² + b² + 2ab

(√3)² + (√2)² + 2√3 √2

= 3 + 2 + 2√6

= 5 + 2√6

Solving denominator  using a² - b² = ( a + b)(a - b)

(√3)² - (√2)²

=3 - 2

=1

(√3 + √2)/ (√3 - √2)   = (5 + 2√6)/1

=5 + 2√6

comparing with

a + b√6

a = 5

b =2

value of a and b

a = 5

b = 2

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