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Chapter 8: Q. 8.116 (page 814)

Solve:y-5+5=y.

Short Answer

Expert verified

The solutions are,y=6andy=5.

Step by step solution

01

Step 1 Given equation is,

y-5+5=y.

The product of Binomial squares pattern is given by,

a-b2=a2-2ab+b2.

The objective is, we need to find the solution for the given equation.

To isolate the radical, subtract 5on both sides.

y-5+5-5=y-5y-5=y-5

02

Step 2 Now square on both sides.

y-5=y-52

Now use the product of binomial square pattern formula on the right side of the equation.

y-5=y2-2y5+52y-5=y2-10y+25

Simplify the obtained equation.

y2-10y+25-y+5=0y2-11y+30=0

Now factorize it.

y-6y-5=0

Now use the zero product property.

y-6=0y=6y-5=0y=5

03

Step 3 Let us check the answer.

Substitute y=6into the equation y-5+5=y.

6-5+5=61+5=61+5=66=6

which is true.

Substitute y=5into the equation y-5+5=y.

5-5+5=50+5=55=5

which is true.

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