To solve: y230=y15+12

Question

limacarp4 · Accepted Answer

Calculation:
Multiply by 30 on both sides,

30 \cdot \frac{y^{2}}{30} = (\frac{y}{15} + \frac{1}{2}) 30

By distributive property,

(\frac{y}{15} + \frac{1}{2}) 30 = \frac{y}{15} \cdot 30 + \frac{1}{2} \cdot 30

(\frac{y}{15} + \frac{1}{2}) 30 = 2 y + 15

30 \cdot \frac{y^{2}}{30} = y^{2}

y^{2} = 2 y + 15

Subtract

- 2 y - 15

on both sides,

y^{2} - 2 y - 15 = 2 y + 15 - 2 y - 15

y^{2} - 2 y - 15 = 0

Split the middle term

- 2 y as - 5 y and + 3 y

Replace -2y with

- 5 y + 3 y \in y^{2} - 2 y - 15 = 0

,

y^{2} - 5 y + 3 y - 15 = 0

The above equation can be written as

y \cdot y - 5 \cdot y + 3 \cdot 3 - 3 \cdot 5

Apply distributive property for first two terms and last two terms,

y \cdot y - 5 \cdot y + 3 \cdot y - 3 \cdot 5 = y (y - 5) + 3 (y - 5)

Again apply distributive property for

y (y - 5) + 3 (y - 5)

y (y - 5) + 3 (y - 5) = (y + 3) (y - 5)

So the factors are

(y + 3) and (y - 5)

y^{2} - 2 y - 15 = (y + 3) (y - 5)

To find the value of y,
Take

y - 5 = 0

Add 5 on both sides,

y - 5 + 5 = 0 + 5

Add the like terms,

y = 5

Take

y + 3 = 0

Subtract 3 on both sides,

y + 3 - 3 = 0 - 3

Add the like terms,

y = - 3

The factors are

y = - 3 and y = 5

So, the values of y are -3 and 5.

sonorous9n · Accepted Answer

y230⋅30=y15⋅30+12⋅30  y2=2y+15  y2−15=2y+15−15  y2−15=2y  y2−15−2y=2y−2y  y2−2y−15=0  y1,2=−(−2)±(−2)2−4⋅1⋅(−15)2⋅1  y1,2=−(−2)±82⋅1  y=−(−2)+82⋅1,y2=−(−2)−82⋅1  y=−(−2)+82⋅1:5  y=−(−2)−82⋅1:−3  y=5,y=−3

karton · Accepted Answer

y230=y15+12y2=2y+15y2−2y=15y2−2y−15=0a+b=−2ab=−151,−153,−51−15=−143−5=−2a=−5b=3(y−5)(y+3)y=5y=−3