Solving Equations Worksheet1 Solution7





In this page solving equations worksheet1 solution7 we are going to see solution of practice questions.

Question 7:

When √(2 z + 1) + √(3 z + 4) = 7 the value of z is given by

Solution:

√(2 z + 1) + √(3 z + 4) = 7

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

[√(2 z + 1) + √(3 z + 4)]² = 7²

[√(2 z + 1)]² + [√(3 z + 4)]² + 2√(2 z + 1) (3 z + 4) = 49

2 z + 1 + 3 z + 4 + 2√(6 z² + 11 z + 4) = 49

5 z + 5 + 2√(6 z² + 11 z + 4) = 49

2√(6 z² + 11 z + 4) = 49 - 5 z - 5

 2√(6 z² + 11 z + 4) = 44 - 5 z

now we are going to take squares on both sides to remove square root on left side

 [2√(6 z² + 11 z + 4)]² = (44 - 5 z)²

4 (6 z² + 11 z + 4) = 44² - 2 (44) (5 z) + (5z)²

24 z² + 44 z + 16 = 1936 - 440 z + 25 z²

25 z² - 24 z² - 440 z - 44 z + 1936 - 16 = 0

z² - 484 z + 1920 = 0

z² - 480 z - 4 z + 1920 = 0

z (z - 480) - 4 (z - 480) = 0

(z - 4) (z - 480) = 0

 z - 4 = 0          z - 480 = 0

    z = 4                   z = 480

solution are x = 4 and x = 480

Therefore the correct option is option (C)

(A)   1

(B)   2

(C)   3

(D)   4

solving equations worksheet1 solution7 solving equations worksheet1 solution7