Question

solve the following questions please ​

Answer 1

SEE THE AATACHMENT YOUR ANSWER IS THIS AND I THINK IT IS CORRECT

#TOGETHER WE GO FAR✔✔

Answer 2

If we let x and y be the two numbers, then the sum is x + y and the G.M. is 6√(xy). This givs:  

x + y = 6√(xy)  

==> (x + y)^2 = [6√(xy)]^2, from squaring  

==> x^2 + 2xy + y^2 = 36xy  

==> x^2 - 34xy + y^2 = 0.

By the Quadratic Formula:  

(b^2 - 4ac = (-34y)^2 - 4(1)(y^2) = 1152y^2)

x = [-b +/- √(b^2 - 4ac)]/(2a)  

= [34y +/- √(1152y^2)]/2  

= (34y +/- 24y√2)/2  

= (17 +/- 12√2)y.

However, since xy > 0, we require that the coefficient of y is positive. Thus:  

x = (17 + 12√2)y.  

This shows that:  

x/y = 17 + 12√2 = (3 + 2√2)/(3 - 2√2), as required.  

I hope this helps!