Aptitude - Square Root and Cube Root - Discussion

Using , (x+y)^2 = x^2 +y^2 -2xy

So, x^2 +y^2 = (x+y) ^2 - 2xy ---> (I)

(X+y) = (√3 + 1) /(√3 - 1) + (√3 - 1) /(√3 + 1).

On taking LCM,
(X+y) = {(√3 + 1)^2 +(√3 - 1)^2}/(√3 - 1)(√3 +1).

(X+y) =(3+1-2√3 +3+1-2√3) /[(√3) ^2 - 1^2].

(X+y) = 8/(3-1),
(X+y) = 8/2,
(x+y) = 4.

Now, XY = {(√3 + 1) /(√3 - 1)} * {(√3 - 1) /(√3 + 1)},
XY = 1.

Now putting values of (X+y) & XY in equation (I)
x^2 + y^2 = (x+y) ^2 - 2xy ---> (I)
x^2 + y^2 = (4) ^2 - 2,
x^2 + y^2 = 16 - 2,
x^2 + y^2 = 14.

Answer is 14.

Hello priya and jaggu ,we can get 2(4+3) as follows:

(a+b)2+(a-b)2=2(a+b).................(1)

Let us prove this

Take LHS of eq(1)

a2+b2+2ab+a2+b2-2ab

Here +2ab and -2ab get cancelled and the remaining can be written as

2a2+2b2

2(a2+b2)


So here a=2 and b=rt3

2(4+3)

(a+b)2+(a-b)2 = 2(a2+b2).

Here a = 2 =>a2 = 4; b = 3^(1/2) =>b2 = 3.

=>2(4+3).

=>2(7).

=>14.

I think this is the correct one because this is the model of rationalization. If this is not the correct answer please explain.

How would you get the answer as 2?

This is correct: 14

x = (3 + 1) x (3 + 1) = (3 + 1)2
= 3 + 1 + 23 = 2 + 3.
(3 - 1) (3 + 1) (3 - 1) 2.

y = (3 - 1) x (3 - 1) = (3 - 1)2 = 3 + 1 - 23 = 2 - 3.
(3 + 1) (3 - 1) (3 - 1) 2,
x2 + y2 = (2 + 3)2 + (2 - 3)2,
= 2(4 + 3),
= 14.

Root 3 -> 1.732.

1.732+1=2.732.
1.732-1=0.732.

2.732/0.732=3.7322.
0.732/2.732=0.2679.

(3.7322)^2=13.929 & (0.2679)^2=0.0192.

Add 13.929+0.0192=13.9482 is near by 14.

So answer is 14.
Are you clear now friends.

@All.

Here, as whatever power of 1, it remains 1, simply;
(3)^1/2 +1 = (4)^1/2 = 2;
(3)^1/2 - 1 = (2)^1/2,
Thereby X = (2)^1/2 & Y = 1/(2)^1/2,
X^2 = 2 & Y^2 = 1/2.
Ans 2.5.

Hello gaurav and tank mayur.

This is the process of rationalization.

The denominator is multiplied and divided to selected value.

Hope you understand.

Its called conjugate . + in denominoter means u have to multiply & divide the same number but put - sign. denominoter - sign means put + vice versa.

Solve by the normal method using formula,

(a+b)2 = a2 + 2ab + b2.

(a-b)2 = a2 - 2ab + b2.

By using this formula you will get,

8 + 6 = 14.

Could understand how {(3+2)/(3-2) }*{ (3+2)/(3+2)/(3+2)} = (3+2)^2/ (3-2), isn't it should be (3+2)^2/(3^2-1^2)? Please inform me asap.