Question

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 - 10x T/F for each

Answer 1

We have to determine if the sets of quadratics are equivalent:
A ) x² - 10 x - 14 = 0  and ( 2 x - 10 )² = 156
( 2 x - 10 )² - 156 = 0
4 x² - 40 x + 100 - 156 = 0
4 x² - 40 x - 56 = 0 / : 4
x² - 10 x - 14 = 0           T ( True )
B ) ( x - 10 )² = 68  and x² - 20 x = - 32
( x - 10 )² = 68
x² - 20 x + 100 = 68
x² - 20 x = 68 - 100
x² - 20 x = - 32              T ( True )
C ) x² - 6 x = 247 and ( x - 3 )² = 256
( x - 3 )² = 256
x² - 6 x + 9 = 256
x² - 6 x = 247              T ( True )
D ) ( x + 5 )² = 65  and   x² = 90 - 10 x
( x + 5 )² = 65
x² + 10 x + 25 = 65
x² = 65 - 25 - 10 x
x² = 40 - 10 x                F ( False )