Question

solve the following equation √ x²-3x= 4x²-12x-3 .....​

Answer 1

Answer:

x = (3 ± √13)/2

Step-by-step explanation:

Given: √(x² - 3x) = 4x² - 12x - 3 = 4(x² - 3x) - 3

ii) Let x² - 3x = y;

So the given one reduces to: √y = 4y - 3

iii) Squaring both sides, y = 16y² + 9 - 24y

Rearranging and simplifying, 16y² - 25y + 9 = 0

Factorizing, (16y - 9)(y - 1) = 0

==> Either y = 9/16 or y = 1

When y = 9/16, the equation √y = 4y - 3, is not getting verified.

[Left side = 3/4, while right side = -3/4]

So this value is discarded.

When y = 1, the equation √y = 4y - 3 is getting verified.

So we have only one solution for y = 1

iv) Thus at y = 1, we have, x² - 3x = 1

==> x² - 3x - 1 = 0

Solving by using quadratic formula,

x = (3 ± √13)/2

Answer: x = (3 ± √13)/2

Answer 2

Answer:

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