Question

hi!!!!
ans . it and solve all questions

Answer 1

(1)

$Given : x + \frac{1}{x} = \sqrt{5}$

On squaring both sides, we get

= > x^2 + 1/x^2 + 2 * x * 1/x = 5

= > x^2 + 1/x^2 + 2 = 5

= > x^2 + 1/x^2 = 5 - 2

= > x^2 + 1/x^2 = 3.



(2) 

Given 9x^2 + 25y^2 = 181

= > (3x)^2 + (5y)^2 + 2(3x)(5y) - 2(3x)(5y) = 181

= > (3x)^2 + (5y)^2 + 30xy - 30xy = 181

= > (3x + 5y)^2 = 181 + 30xy

= > (3x + 5y)^2 = 181 + 30(-6)

= > (3x + 5y)^2 = 181 - 180

= > (3x + 5y)^2 = 1

= > (3x + 5y) = +1, - 1.



(3) 

Given a + b = 12, ab = 32.

We know that a^2 + b^2 = (a + b)^2 - 2ab

                                          = (12)^2 - 2(32)

                                          = 144 - 64

                                          = 80.


Therefore the value of a^2 + b^2 = 80.


(4) 

Given 2x + 3y = 8 and xy = -3.

On squaring both sides, we get

= > (2x + 3y)^2 = (8)^2

= > 4x^2 + 9y^2 + 12xy = 64

= > 4x^2 + 9y^2 + 12(2) = 64

=  > 4x^2 + 9y^2 + 24 = 64

= > 4x^2 + 9y^2 = 64 - 24

= > 4x^2 + 9y^2 = 40.


Hope this helps!

Answer 2

Answer:

see.....siddhartrao solved your question.....and that's the perfect answer