Question

Brainly challenge for all the genius.......50 mark ques. . ..... If 2 Root 6 - root 5 /root 45 - root 24 =a+b root 30 <br />Then find a, b in easiest way according to 9th class.
Please help me................

Answer 1

Heya !!!

2✓6 - ✓5 / ✓45 - ✓24 = A + B✓30

LHS = 2✓6 - ✓5 / ✓45 - ✓24

=> 2✓6 - ✓5 / 3✓5 - 2✓6

Rationalising the denominator 3✓5 - 2✓6

=> 2✓6 - ✓5 / 3✓5 - 2✓3 × 3✓5 + 2✓6/3✓5 + 2✓6

=>(2✓6 - ✓5)(3✓5+2✓6)/ (3✓5- 2✓6)(3✓5 + 2✓6)

=> 2✓6( 3✓5+2✓6)-✓5( 3✓5 + 2✓6)/(3✓5)² -(2✓6)²

=> 6✓30 + 24 - 15 - 2✓30 / 45 - 24

=> 4✓30 + 9/24

=> 9 + 4✓30/24

Now,

LHS = RHS

9 + 4✓30/24= A + B✓30

Clearly,

A = 9/24 and B = 4/24 = 1/6

Answer 2

Answer:

Hello !!!

Step-by-step explanation:

Here is your answer:-

2✓6 - ✓5 / ✓45 - ✓24 = A + B✓30

LHS = 2✓6 - ✓5 / ✓45 - ✓24

=> 2✓6 - ✓5 / 3✓5 - 2✓6

Rationalising the denominator 3✓5 - 2✓6

=> 2✓6 - ✓5 / 3✓5 - 2✓3 × 3✓5 + 2✓6/3✓5 + 2✓6

=>(2✓6 - ✓5)(3✓5+2✓6)/ (3✓5- 2✓6)(3✓5 + 2✓6)

=> 2✓6( 3✓5+2✓6)-✓5( 3✓5 + 2✓6)/(3✓5)² -(2✓6)²

=> 6✓30 + 24 - 15 - 2✓30 / 45 - 24

=> 4✓30 + 9/24

=> 9 + 4✓30/24

Now,

LHS = RHS

9 + 4✓30/24= A + B✓30

Clearly,

A = 9/24 and B = 4/24 = 1/6