Question

HELP ME PLS

1)if k=7+8/k what is the value of k^2+64/k^2
A. 33
B. 49
C. 64
D. 65


2) 18-3w/w+6=w^2/w+6
which of the following represents the sum of all possible solutions to the equation above?
A. -9
B. -3
C. 3
D. 9

Answer 1

1. The required "option D) 65" is correct.

2. The required "option B)" is correct.

Step-by-step explanation:

1. We have,

k =$7+\dfrac{8}{k}$  

⇒ k - $\dfrac{8}{k}$ = 7           ......... (1)

To find, the value of $k^{2}+\dfrac{64}{k^2}$ = ?

Squaring (1) in both sides, we get

$(k -\dfrac{8}{k})^2=7^2$

⇒ $k^{2}+\dfrac{64}{k^2}$  $-2.k.\dfrac{8}{k}=49$

⇒ $k^{2}+\dfrac{64}{k^2}$ = 49 + 16 = 65

Thus, the required "option D) 65" is correct.

2. We have,

$\dfrac{18-3w}{w+6}=\dfrac{w^2}{w+6}$

Mutiplying both sides (w + 6), we get

⇒ $18-3w=w^2$

⇒ $w^2$ + 3w - 18 = 0

⇒ $w^2$ + 6w -3 w - 18 = 0

⇒ (w + 6)(w - 3) = 0

⇒ w = - 6 or, 3

∴ The sum of all possible solutions = - 6 + 3 = - 3

Thus, the required "option B)" is correct.