Aptitude - Square Root and Cube Root - Discussion

The value of √3 is 1.732. By applying this, we will get the answer.

x2 + y2 = (2 + √3)2 + (2 - √3)2.
= (4+2*2*√3+3) + (4 - 2*2*√3+3),
= (4+3) + (4+3),
= 2(4+3).

@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.

Can someone clearly explain this in step by step?

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.

x2+y2=(x-y)2+2xy, can we use this formula?

Anyone explain me.

Hello, I just didn't understand how is 3+1+2√3/2 = 2+√3.

Please explain.

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.

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.

(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?