Sec 2 Maths

kkhing SG

Given that 6/V -15V = 24, find the values of 5V + 2/V

Forbiddensinner SG

Given that 6/V -15V = 24, find the values of 5V + 2/V

6/V - 15V = 24
6 - 15V^2 = 24V
15V^2 + 24V = 6
5V^2 + 8V = 2
5V^2 + 8V - 2 = 0
5(V^2 + 8V/5) - 2 = 0
5(V + 4/5)^2 - 16/5 - 2 = 0
5(V + 4/5)^2 = 26/5
(V + 4/5)^2 = 26/25
V + 4/5 = sqrt(26) / 5 or = -sqrt(26) / 5
V = [sqrt(26) - 4] / 5 or = [-sqrt(26) - 4] / 5

Okay, the first part is done.
Just substitute the above values in to get the two possible values of 5V + 2/V.

dreamer87 SG

My solution :
6/V - 15V = 24
6 - 15V^2 = 24V
2- 5V^2 = 8V
5V^2 +8V - 2 = 0
V = [-8 + sqrt(8^2 - 4(5)(-2))] / 10 or [-8 - sqrt(8^2 - 4(5)(-2))] / 10
V = [-8 + sqrt(104)] / 10 or [-8 - sqrt(104)] / 10

104 = 2^3 * 13 = 2sqrt(26)
V = -4/5 + sqrt(26)/5 or -4/5 - sqrt(26)/5

frekiwang SG

I thought I already answered you somewhere else.

6/V - 15V = 24

2/V - 5V = 8

Square both side, we have
(2/V)^2 - 2(2/V)(5V) + (5V)^2 = 64

Add 4(2/V)(5V) to both sides to complete the square

(2/V)^2 + 2(2/V)(5V) + (5V)^2 = 64 + 4(2/V)(5V)

(2/V+5V)^2 = 104

2/V + 5V = +/- sqrt(104)