Solve the equation

Question

17) 4t²/ 5 = 11t/ 5 + 13/10 

the solution is t= 



15) Solve 

√ (53-x)=x+3. 

x=

Answer 1

17). The equation is 4t^2/5 = 11t/5 + 13/10.

4t^2/5 - 11t/5 = 13/10

(4t^2 - 11t)/5 = 13/10

4t^2 - 11t = 13/2

2(4t^2 - 11t) = 13

8t^2 - 22t - 13 = 0

By factor by grouping.

8t^2 + 4t - 26t - 13 = 0

4t(2t + 1) - 13(2t + 1) = 0

Factor : (2t + 1)(4t - 13) = 0

Apply zero product property.

2t + 1 = 0 and 4t - 13 = 0

2t = - 1 and 4t = 13

t = - 1/2 and t = 13/4

The solutions are t = - 1/2 and t = 13/4.

15).

The equation is √(53 - x) = x + 3.

53 - x = (x + 3)^2

53 - x = x^2 + 6x + 9

x^2 + 7x - 44 = 0

By factor by grouping.

x^2 + 11x - 4x - 44 = 0

x(x + 11) - 4(x + 11) = 0

Factor : (x + 11)(x - 4) = 0

Apply zero product property.

x + 11 = 0 and x - 4 = 0

x = - 11 andx = 4

The solutions are x = - 11 and x = 4.

Comments

The two solutions are x = - 11 and x = 4.

Here the - 11 is called extraneous solution, since the number - 11 does not satisfy the original equation.

√(53 - x) = x + 3

√[53 - (- 11)] = (- 11) + 3

√[64] = - 8

8 = - 8, this is false statement.

Substitute the value of x = 4 in the original equation.

√(53 - x) = x + 3

√[53 - (4)] = (4) + 3

√[49] = 7

7 = 7, this is true statement.

The solution of the equation is 4.