Question

3-√5×3-2√5= a√5-19/11 , find values of a​

Answer 1

Answer:

Step-by-step explanation:

=(3-√5)/(3+2√5)

=(3-√5)/(3+2√5)×(3-2√5)/(3-2√5)

=(3-√5)(3-2√5)/(3+2√5)(3-2√5)

=[3(3-2√5)-√5(3-2√5)]/(3²-(2√5)²

=(3²-6√5-3√5+2(5))/(9-4(5))

=(9-9√5+10)/(9-20)

=(19-9√5)/(-11)

=–(19-9√5)/ 11

= –(19-9√5)/11

=(-19+9√5)/11

=(9√5-19)/11

=9√5/11 - 19/11 = a√5-19/11

Therefore,a=9/11

If it is (a√5-19)/11 then a=9

But according to question,a√5-19/11

So,answer is 9/11

Answer 2

Find the value of a in (3 - √5) / (3 + 2√5) = a√5 - 19/11

Solution:

Given, the expression is (3 - √5) / (3 + 2√5) = a√5 - 19/11

We have to find the value of a.

Considering LHS,

LHS: (3 - √5) / (3 + 2√5)

By taking conjugate,

(3 - √5) / (3 + 2√5) = (3 - √5) / (3 + 2√5) × (3 - 2√5) / (3 - 2√5)

= (3 - √5)(3 - 2√5) / (3 + 2√5)(3 - 2√5)

By using algebraic identity,

(a² - b²) = (a - b)(a + b)

(3 + 2√5)(3 - 2√5) = (3)² - (2√5)²

= 9 - 4(5)

= 9 - 20

= -11

So, (3 - √5)(3 - 2√5) / (3 + 2√5)(3 - 2√5) = (3 - √5)(3 - 2√5) / (-11)

By multiplicative and distributive property,

(3 - √5)(3 - 2√5) = 3(3) - 3(2√5) - 3(√5) + 2√5(√5)

= 9 - 6√5 - 3√5 + 2(5)

= 9 - 9√5 + 10

= 19 - 9√5

Now, (3 - √5)(3 - 2√5) / (-11) = (19 - 9√5) / (-11)

= 19/(-11) - 9√5/(-11)

= 9√5/11 - 19/11

So, a√5 - 19/11 = 9√5/11 - 19/11

a√5 - 19/11 + 19/11 = 9√5/11

a√5 = 9√5/11

a = 9/11

Therefore, the value of a is 9/11

HOPE THIS HELPS YOU