What must be added to 4x2 - 4 to make it a perfect square?
−1x2
1x2
1
-1
Correct answer is B
(2x −142 = 4x2 + 1x2 - 4
what must be added is +1x2
16
14
12
9
Correct answer is B
x + 1x = 4, find x2 + 1x2
= (x + 1x)2 = x2 + 1x2 + 2
x2 + 1x2 = ( x + 1x2)2 - 2
= (4)2 - 2
= 16 - 2
= 14
Divide x3 - 2x2 - 5x + 6 by (x - 1)
x2 - x - 6
x2 - 5x + 6
x2 - 7x + 6
x2 - 5x - 6
Correct answer is A
Step 1: Just multiply each of the options by ( x - 1 )
Step 2: Then collect like terms to derive the same equation found in the question.
Hope this helps!
If a2 + b2 = 16 and 2ab = 7.Find all the possible values of (a - b)
3, -3
2, -2
1, -1
3, -1
Correct answer is A
a2 + b2 = 16 and 2ab = 7
To find all possible values = (a - b)2 + b2 - 2ab
Substituting the given values = (a - b)2
= 16 - 7
= 9
(a - b) = ±9
= ±3
OR a - b = 3, -3
Factorize 9(x + y)2 - 4(x - y)2
(x + y)(5x + y)
(x + y)2
(x + 5y)(5x + y)
5(x + y)2
Correct answer is C
9(x + y)2 - 4(x - y)2
Using difference of two squares which says
a2 - b2 = (a + b)(a - b) = 9(x + y)2 - 4(x - y)2
= [3(x + y)]2 - [2(x - y)]-2
= [3(x + y) + 2(x - y) + 2(x - y)][3(x + y) - 2(x - y)]
= [3x +3y + 2x - 2y][3x + 3y - 2x + 2y]
= (5x + y)(x + 5y)