Determine if the following sets of quadratics are equivalent. Choose true or false. x 2 - 10x + 14 = 0 and (2x - 10)2 = 156 (x - 10)2 = 68 and x 2 - 20x = -32 x 2 - 6x = 247 and (x - 3)2 = 256 (x + 5)2 = 65 and x 2 = 90 - 10
Accepted Solution
A:
A ) x² - 10 x - 14 = 0 and ( 2 x - 10 )² = 156 T ( True ) ( 2 x - 10 )² - 156 = 04 x² - 40 x + 100 - 156 = 04 x² - 40 x - 56 = 0 / : 4x² - 10 x - 14 = 0
B ) ( x - 10 )² = 68 and x² - 20 x = - 32 / T ( True ) ( x - 10 )² = 68 x² - 20 x + 100 = 68x² - 20 x = 68 - 100x² - 20 x = - 32
C ) x² - 6 x = 247 and ( x - 3 )² = 256 / T ( True ) ( x - 3 )² = 256x² - 6 x + 9 = 256x² - 6 x = 247
D ) ( x + 5 )² = 65 and x² = 90 - 10 x / F ( False ) ( x + 5 )² = 65x² + 10 x + 25 = 65x² = 65 - 25 - 10 xx² = 40 - 10 x