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Chapter 9: Q.187 (page 906)

In the following exercises, solve equations in Quadratic Form for x + 8x12+ 7 = 0.

Short Answer

Expert verified

The equation has No solution for x∈R.

Step by step solution

01

Step 1. Given Information.

The given equation is x + 8x12+ 7 = 0.

02

Step 2. Remove square roots

Simplify x + 8x12+ 7 = 0x+7=-8x12

Squaring both sides , we get:-

(x+7)2=-8x122x2+14x+49=64xx2+14x-64x+49=0x2-50x+49=0

03

Step 3. Solving quadratic equation .

Using Quadratic formula :-

x2-50x+49=0

x1, 2=--50±-502-4· 1· 492· 1x1, 2=--50± 482· 1x1=--50+482· 1, x2=--50-482· 1x=49, x=1

04

Step 4. Verifying the solutions.

Substitute the value of x=49in x + 8x12+ 7 = 0, we get:-

49 + 84912+ 7 = 49+8×7+7 49+8×7+7=112112≠0

Similarly , Substitute x=1in the equation x + 8x12+ 7 = 0, we get:-

1 + 8112+ 7 = 1+8+71+8+7=1616≠0

Since, for x=49, x=1the conditions are not satisfied. Therefore, There are No Solutions for the equation.

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