Question

Which of the following are solutions to the equation below?

Answer 1

Option C and D, i.e. -4/5 and 4/5

Explanation:

Given is 25x² -16 = 0

(5x)² - 4² = 0

Using the formula "Difference of squares" given as follows:-

a² - b² = (a-b)(a+b)

(5x)² - 4² = (5x-4)(5x+4)

So (5x-4)(5x+4) = 0

Using "Null product" property given as follows:-

If A*B = 0, then A=0 or B=0.

So, (5x-4)(5x+4) = 0 means (5x-4)=0 or (5x+4)=0

Solving for x values:-

5x - 4 = 0 and 5x + 4 = 0

5x = 4 and 5x = -4

x = 4/5 and x = -4/5

Hence, options C and D are correct, i.e. -4/5 and 4/5.

Answer 2

c) -4/5

d) 4/5

Explanation:

The given equation is 25x^2 -16 = 0

Adding 16 on both sides, we get

25x^2 = 16

Dividing both sides by 25, we get

x^2 = 16/25

Taking square root on both sides, we get

x = √(16/25)

x = ±4/5

Therefore, x = 4/5 and x = -4/5

Answers: C) and D)

Hope this will helpful to understand the concept.

Thank you.