If a2 + b2 = 15 and ab = 3, then the value of (a-b)2 is:
A. 21 B. 18 C. 12 D. 9 E. 3
I really don't understand how I could possibly get this... can I please get some help?
please, help me I've been trying to figure this out for a while, but nothing works
suppose we expand (a-b)^2
(a-b)^ = a^2 + 2ab + b^2
= a^2 + b^2 + 2ab we know those..
= 15 + 2(3)
= 21
To find the value of (a-b)2, we can start by expanding the expression (a-b)2 using the binomial formula. The formula states that (a-b)2 = a2 - 2ab + b2.
Given that a2 + b2 = 15 and ab = 3, we can substitute these values into the expression. We have:
(a-b)2 = a2 - 2ab + b2
= 15 - 2(3) + b2 (substituting a2 + b2 = 15)
= 15 - 6 + b2
= 9 + b2
Now we need to find the value of b2. To do that, we can divide both sides of the equation ab = 3 by b:
ab = 3
a = 3/b
Substituting this value back into the expression for (a-b)2:
(a-b)2 = 9 + b2
= 9 + (3/b)2 (substituting a = 3/b)
= 9 + 9/b2
= (9b2 + 9)/b2
To simplify further, we can combine the terms inside the parentheses:
(a-b)2 = (9b2 + 9)/b2
= 9(b2 + 1)/b2
Now, we can conclude that the value of (a-b)2 is 9(b2 + 1)/b2. Since we don't have any specific information about the value of b, we cannot determine the exact value of (a-b)2. Therefore, the answer cannot be determined from the given information, and none of the options A, B, C, D, or E is correct.