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Chapter 9: Q.182 (page 906)

In the following exercises, solve equations in Quadratic Form for x23鈥�鈭�鈥�11x13+鈥�30鈥�=鈥�0.

Short Answer

Expert verified

The solution of the quadratic equation is x=216,鈥�x=125.

Step by step solution

01

Step 1. Given Information.

The given equation is x23鈥�鈭�鈥�11x13+鈥�30鈥�=鈥�0.

02

Step 2. Simplifying .

Simplifying x23鈥�鈭�鈥�11x13+鈥�30鈥�=鈥�0

x132-11x13+30=0

Substitute u=x13, we get:-

u2-11u+30=0

03

Step 3. Solving quadratic equation .

Using Quadratic Formula:-

u1,鈥�2=--11卤-112-4路鈥�1路鈥�302路鈥�1u1,鈥�2=--11卤鈥�12路鈥�1u1=--11+12路鈥�1,鈥�u2=--11-12路鈥�1u=6,鈥�u=5

04

Step 4. Simplify .

Solve for

x13=6;x=216x13=5;x=125

Therefore, The solution are x=216,鈥�x=125 .

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