Mathematics Questions And Answers! Basic Algebra Equation Solution, Equation Solving Method.

Q.NO.01: How do you solve for x in the given proportion: x/5 = 20/x?

Solution:

x/5 = 20/x

Apply cross multiplication:

x^2 = 100

Taking square root on both sides:

X = +10 

X = - 10

Q.NO.02: In the equation "9ˣ - 4.3ˣ⁺¹ + 3³ = 0", what is the value of X?

Solution:

Given that:

9ˣ - 4.3ˣ⁺¹ + 3³ = 0

Convert values into power:

3^2x - 4.3^x+1 + 3^3 =0 …..equ1

Let 3^x = y …...equ2

Put it in equ1

y^2 - 4.3.y + 27= 0

y^2 - 12y + 27 = 0

Apply factorization 

y^2 -9y -3y + 27 = 0

y (y - 9) -3 (y - 9) = 0

(y - 9) (y - 3) = 0 ….. equ3 

From equ2 y = 3^x

Put it in equ3

(3^x - 9) (3^x - 3) = 0

Or

3^x - 9 = 0             3^x - 3 = 0

3^x = 9                  3^x = 3

3^x = 3^2              3^x = 3^1

If bases are equal the power will be equal to

x = 2 or x = 1

Q.NO.03: What is the solution to the equation 27^(x-2) =3^ (x+6)?

Solution:

27^(x-2) = 3^(x+6)

Convert 27 into power 3:

3^3(x-2) = 3^(x+6)

If bases are equal than power is also equal

3(x-2) = x+6

3x - 6 = x + 6

3x - x = 6 + 6

2x = 12

x = 6

Q.NO.04: Point lies on the circle whose equation is (x - 3) ² + (y + 3) ² = 45?

Solution:

All points which satisfy the equation lies on the circle.

For example (x , y) = (9 , 0)

Q.NO.05: How do you obtain the general solution of the following unless otherwise instructed: (D³+2D²+D+2) y=0?

Solution:

The characteristic of the equation:

D³ + 2D² + D + 2 = 0

Taking common between two values:

D² (D + 2) +1 (D + 2) = 0

(D² + 1) (D + 1) = 0

For solution:

D² + 1 = 0

D² = -1

D = under root-1, under root +1

Or

D + 1 = 0

D = -1

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How to solve the step-one equation? Lesson