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Chapter 9: Q.186 (page 906)

In the following exercises, solve equations in Quadratic Form for 20x23鈥�鈭�鈥�23x13鈥�+鈥�6鈥�=鈥�0.

Short Answer

Expert verified

The solution of the equation is x=2764,鈥�x=8125.

Step by step solution

01

Step 1. Given Information.

The given equation is 20x23鈥�鈭�鈥�23x13鈥�+鈥�6鈥�=鈥�0.

02

Step 2. Simplifying .

Simplify 20x23鈥�鈭�鈥�23x13鈥�+鈥�6鈥�=鈥�0

20x132-23x13+6=0

Substitute u=x13, we get:-

20u2-23u+6=0

03

Step 3. Solving quadratic equation .

Using quadratic formula:-

20u2-23u+6=0

20u2-23u+6=0

u1,鈥�2=--23卤-232-4路鈥�20路鈥�62路鈥�20u1,鈥�2=--23卤鈥�72路鈥�20u1=--23+72路鈥�20,鈥�u2=--23-72路鈥�20u=34,鈥�u=25

04

Step 4. Simplify

Solve for

x13=34;x=2764x13=25;x=8125

Therefore, The solution of the equation is x=2764,鈥�x=8125.

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