Friday, September 27, 2013

Algebra



4x2 + y2 = 10   ---------------------  (1)
2x + y = 4    ------------------------ (2)



You may find that if you square (2), the square terms will be same as that in (1). This will help us to extract the value of xy.

So, lets’ first square Eq (2)

We get 4x2 + y2 + 4xy = 16  --------- (3)

Substitute Eq (1) in (3), we get

10 + 4xy = 16

Or, xy = 6/4  ---------------- (4)

Now whenever we find a situation here the value of a + b and ab is given, we find a – b using the good old formulae

( a – b)2 = (a + b)2 – 4ab

Applying this concept, we get

(2x – y)2 = (2x + y)2 – 4.2x.y

Now, substitute the values on RHS of equation  with values from (2) and (4)

(2x – y)2 = 42 – 4.2.6/4 = 4

Or, 2x – y = 2  ------------------------- (5)

Now, simply solve equation (2) and (5) by adding the two equations

We get 4x = 6

Or x = 3/2

Therefore, y = 1

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