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Chapter 6: Q. 436 (page 636)

In the following exercises, solve.

2y3+2y2=12y

Short Answer

Expert verified

Answer isy=0,y=2,y=-3

Step by step solution

01

Step 1. Given

The equation is2y3+2y2=12y

02

Step 2. Simplify the equation

2y3+2y2=12y2y3+2y2-12y=0y3+y2-6y=0y(y2+y-6)=0y(y2+3y-2y-6)=0y(y(y+3)-2(y+3))=0y(y+3)(y-2)=0

So,

y=0

and

y+3=0y=-3

and

y-2=0y=2

03

Step 3. Check all the values

Put y=0

2y3+2y2=12y2(0)3+2(0)2=12(0)0=0

True

Now put role="math" localid="1644656268781" y=-3in the original equation,

2y3+2y2=12y2(-3)3+2(-3)2=12脳-3-54+18=-36-36=-36

True

Now put y=2in the original equation,

2y3+2y2=12y2(2)3+2(2)2=12脳216+8=2424=24

True

04

Step 4. Required answer

Answer isy=0,y=-3,y=2

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