Solve:
it plz urgent
Answers
Answer:
a) (x-1)(x-3) =15
x²-3x-x+3=15
x²-4x+3=15
x²-4x+3-15=0
x²-4x-12=0
x²-6x+2x-12=0
x(x-6)+2(x-6)=0
(x-6)(x+2)=0
x=6 or x=-2
EXPLANATION.
(1) = (x - 1)(x - 3) = 15.
As we know that,
⇒ x² - 3x - x + 3 = 15.
⇒ x² - 4x + 3 - 15 = 0.
⇒ x² - 4x - 12 = 0.
Factorizes the equation into middle term splits, we get.
⇒ x² - 6x + 2x - 12 = 0.
⇒ x(x - 6) + 2(x - 6) = 0.
⇒ (x + 2)(x - 6) = 0.
⇒ x = - 2 & x = 6.
(2) = x(3x + 1) = 4.
As we know that,
⇒ 3x² + x - 4 = 0.
Factorizes the equation into middle term splits, we get.
⇒ 3x² + 4x - 3x - 4 = 0.
⇒ x(3x + 4) - 1(3x + 4) = 0.
⇒ (x - 1)(3x + 4) = 0.
⇒ x = 1 & x = -4/3.
(3) = x + 1/x = 10/3, x ≠ 0.
As we know that,
⇒ x² + 1/x = 10/3.
⇒ 3(x² + 1) = 10x.
⇒ 3x² + 3 - 10x = 0.
⇒ 3x² - 10x + 3 = 0.
Factorizes the equation into middle term splits, we get.
⇒ 3x² - 9x - x + 3 = 0.
⇒ 3x(x - 3) - 1(x - 3) = 0.
⇒ (3x - 1)(x - 3) = 0.
⇒ x = 1/3 & x = 3.
(4) = 2x - 3/x = 5, x ≠ 0.
As we know that,
⇒ 2x² - 3/x = 5.
⇒ 2x² - 3 = 5x.
⇒ 2x² - 3 - 5x = 0.
⇒ 2x² - 5x - 3 = 0.
Factorizes the equation into middle term splits, we get.
⇒ 2x² - 6x + x - 3 = 0.
⇒ 2x(x - 3) + 1(x - 3) = 0.
⇒ (2x + 1)(x - 3) = 0.
⇒ x = -1/2 & x = 3.
(5) = (x + 3)/(x + 2) = (3x - 7)/(2x - 3), x ≠ 2, 3/2.
As we know that,
⇒ (x + 3)(2x - 3) = (3x - 7)(x + 2).
⇒ 2x² - 3x + 6x - 9 = 3x² + 6x - 7x - 14.
⇒ 2x² + 3x - 9 = 3x² - x - 14.
⇒ 3x² - x - 14 - 2x² - 3x + 9 = 0.
⇒ 3x² - 2x² - x - 3x - 14 + 9 = 0.
⇒ x² - 4x - 5 = 0.
Factorizes the equation into middle term splits, we get.
⇒ x² - 5x + x - 5 = 0.
⇒ x(x - 5) + 1(x - 5) = 0.
⇒ (x + 1)(x - 5) = 0.
⇒ x = - 1 & x = 5.
(6) = (2x)/(5 - 3x) = (5 + 3x)/(8x), x ≠ 0, 5/3.
As we know that,
⇒ (2x)(8x) = (5 + 3x)(5 - 3x).
⇒ 16x² = (5)² - (3x)².
⇒ 16x² = 25 - 9x².
⇒ 16x² + 9x² = 25.
⇒ 25x² = 25.
⇒ x² = 1.
⇒ x = ± 1.