Which of the following are quadratic equations?
(xiii)16x² − 3 = (2x + 5) (5x − 3)
(xiv)(x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)
Answers
SOLUTION :
(xiii) Given : 16x² - 3 = (2x + 5) (5x - 3)
16x² - 3 = 10x² - 6x + 25x - 15
16x² - 3 = 10x² + 19x - 15
16x² - 10x² - 19x - 3 + 15 = 0
6x² - 19x + 12 = 0
The above equation is of the form ax² + bx + c = 0, a ≠ 0, where a = 6 , b = - 19 , c = 12
Hence, the above given equation represents a quadratic equation.
(xiv) Given : (x + 2)³ = x³ - 4
x³ + 2³ + 3x 2 (x+2) = x³ - 4
[(a + b)³ = a³ + b³ + 3ab(a + b)]
x³ + 8 + 6x (x + 2) = x³ - 4
x³ + 8 + 6x² + 12x = x³ - 4
x³ - x³ + 6x² + 12x + 4 + 8 = 0
6x² + 12x + 12 = 0
6(x² + 2x + 2) = 0
x² + 2x + 2 = 0
The above equation is of the form ax² + bx + c = 0, a ≠ 0, where a = 1 , b = 2 , c = 2
Hence, the above given equation represents a quadratic equation.
(xv) Given : x(x + 1) + 8 =(x + 2)(x - 2)
x² + x + 8 = x² - 2²
[(a + b)(a - b) = a² - b²]
x² + x + 8 = x² - 4
x² - x² + x + 8 + 4 = 0
x + 12 = 0
The above equation is not of the form ax² + bx + c = 0, a ≠ 0,because the degree of the equation is of 1 (linear equation).
Hence, the above given equation does not represent a quadratic equation.
HOPE THIS ANSWER WILL HELP YOU…
Which of the following are quadratic equations?
(xiii)16x² − 3 = (2x + 5) (5x − 3)√√ is answer
(xiv)(x + 2)³ = x³ − 4
(xv) x(x + 1) + 8 = (x + 2) (x − 2)