Maths-
General
Easy
Question
If a2 + b2 = z and ab = y, which of the following is equivalent to 4z + 8y ?
- (a + 2b)2
- (2a +2b)2
- (4a + 4b)2
- (4a + 8b)2
The correct answer is: (2a +2b)2
Solution:-
- We have given equations
a2 + b2 = z --------- (1)
ab = y --------- (2)
- We have to find the value of
4z + 8y
- We will put the values of z and y in 4z +8y
4z + 8y = 4(a2 + b2)+ 8(xy)
= 4a2 + 4b2+ 8xy
- We can write 4a2 as (2a)2 as if we squared the term 2a we get 4a2.
- Also, we can write 4b2 as (2b)2 as if we squared the term 2b we get 4b2.
- So, we get
4z + 8y = (2a)2 + (2b)2 + 8xy
- On comparing the RHS with the formula u2+ v2 +2uv= (u + v)2,
We get, u = 2a , v = 2b , 2uv= 2(2a)(2b)
Therefore, 4z + 8y = (2a + 2b)2
- Therefore the correct answer is option(B) (2a + 2b)2.
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