Solving Equations Worksheet1 Solution4





In this page solving equations worksheet1 solution4 we are going to see solution of practice questions.

Question 4:

The  values of x satisfying the equation

√(2 x² + 5 x - 2) - √(2 x² + 5 x - 9) = 1 are

Solution:

For removing the square root on left side first we have to take square on both sides 

[√(2 x² + 5 x - 2) - √(2 x² + 5 x - 9)]² = 1

[√(2x²+5 x-2)]²+[√(2x²+5x-9)]² -2√(2 x²+5x-2)(2x²+5x-9) = 1²

(2x²+5 x-2)+(2x²+5x-9) -2√(2 x²+5x-2)(2x²+5x-9) = 1

4 x² + 10 x - 11 - 1 = 2√(2 x²+5x-2)(2x²+5x-9)

4 x² + 10 x - 12 = 2√(2 x²+5x-2)(2x²+5x-9)

Dividing the whole equation by 2,we get

2 x² + 5 x - 6 = √(2 x²+5x-2)(2x²+5x-9)

(2 x² + 5 x - 6)² = (2 x²+5x-2)(2x²+5x-9)

(2x²)²+(5x)²+(-6)²+2(2x²)(5x)+2(5x)(-6)+2(-6)(2x²)

           = 4x⁴+10x³-18x²+10x³+25x²-45x-4x²-10x+18

4x⁴+25x²+36+20x³-60x-24x²=4x⁴+20x³-22x²+25x²-45x-10x+18

4x⁴+25x²+36+20x³-60x-24x²=4x⁴+20x³+3x²-55x+18

4x⁴ - 4x⁴ + 20x³ - 20x³ + x²- 3x² - 60 x + 55 x + 36 -18 = 0

 -2x² - 5x + 18 = 0

dividing the whole equation by (-1),we get

2x² + 5 x - 18 = 0

Now we are going to factorize this equation

2x² - 4 x + 9 x - 18 = 0

2x (x - 2) + 9 (x - 2) = 0

(2 x + 9) (x - 2) = 0

2 x + 9 = 0            x - 2 = 0

2x = -9                    x = 2

 x = -9/2

solution are x = -9/2 and x = 2

Therefore the correct option is option (B)

(A)  5/2 , -4

(B)  -9/2 , 2

(C)  4/5 , -4

(D)  -1/5 , 3

solving equations worksheet1 solution4 solving equations worksheet1 solution4