Question

7. Simplify the following.
(i) (2x + 3y)(2x - 3y)
(ii) (a-3a+3)
(iii) (a2+a+4(a-2)
(iv) (x - 1)(x-2)(x-3)
(v) (x + y)(x - y)(x2 + y2)​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Answer 2

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