If (a + b) = 4, and ab = 7/4, what is the value of a^2 b^2?

I'm getting answer D...

ab = 7/4

(a+b)^2 = 4^2
a^2 + 2ab + b^2 = 16

(a+b) = 4
7/4b + b = 4
28b + 4b^2 = 16b
4b^2 + 12b = 0
b^2 + 3b = 0
(b+3)*(b-0) = 0

So b is either -3 or 0...

Plugging in these values to a+b = 4...

If b is 0, then:
a+0 = 4
a = 4

If b is 3, then:
a+3 = 4
a = 1

So a^2 - b^2...

It's either:
1^2 - 3^2 = 1-9 = -8

Or...
4^2 - 0^2 = 16

16 (answer D) has to be the answer.

If (a + b) = 4, and ab = 7/4, what is the value of a^2 – b^2?

A. -12
B. 12
C. Either A or B
D. 16
E. None

It is given that (a + b) = 4 and ab = \(\frac{7}{4}\).

The value of \(a^2\) – \( b^2\) is to be calculated. Using standard algebraic identities, \(a^2\) – \(b^2\) = (a + b) (a – b)
Since the value of (a + b) is already given, we need the value of (a – b) to calculate the value of the given expression.

Using standard algebraic identities, \((a – b) ^2\) = \((a + b)^2\) – 4ab.

Substituting the values, \((a -b)^2\) = \((4)^2\) – 4 * \(\frac{7}{4}\) = 16 – 7 = 9
Therefore, (a – b) = 3 or (a – b) = -3

If (a – b) = 3, the value of \(a^2\) – \(b^2\) = 4 * 3 = 12.
If (a – b) = -3, the value of \(a^2\) – \(b^2\) = 4 * -3 = -12.

Therefore, the value of \(a^2\) – \(b^2\) could be 12 or -12.
The correct answer option is C.
 

Hi I have a doubt 
 if we sqaure up a+b=4 then we get
a2 +2(7/4) +b2 =16
a2 +b2 =16-7/2
a2+b2=25/2

cant we substitute a2=12.5-b2 or b2=12.5-a2?­

Hello Bunuel and KarishmaB
Could you please tell me where I am going wrong:


Given that
( a + b ) = 4..........(i) and
ab = 7/4,
We need to find a^2 - b^2, i.e, (a+b)(a-b).

Now, ab = 7/4,
so 2ab = 14/4.......(ii)

(I) - (ii)
a+b - 2ab = 4 - 14/4
(a - b)^2 = 2/4 = 1/2
Thus (a-b) = (+/- [square_root 1/2])....(iii)

Now multiplying (i) by (iii)

(a + b) (a - b) = 4 * (+/- [square_root 1/2]).

Thank you for your time and effort!

The red part is not correct.

a + b - 2ab is not the same as (a - b)^2, which equals a^2 + b^2 - 2ab.

If (a + b) = 4, and ab = 7/4, what is the value of a^2 – b^2?

A. -12
B. 12
C. Either A or B
D. 16
E. None