Aptitude - Square Root and Cube Root - Discussion
Discussion Forum : Square Root and Cube Root - General Questions (Q.No. 7)
7.
| If x = | 3 + 1 | and y = | 3 - 1 | , then the value of (x2 + y2) is: |
| 3 - 1 | 3 + 1 |
Answer: Option
Explanation:
| 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
Discussion:
45 comments Page 5 of 5.
Bhushan said:
6 years ago
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).
= (4+2*2*√3+3) + (4 - 2*2*√3+3),
= (4+3) + (4+3),
= 2(4+3).
(5)
Naomi Mwamba said:
4 years ago
Can someone clearly explain this in step by step?
(3)
Jamshaid said:
3 years ago
@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.
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.
(3)
Chandrakala Rajput said:
2 years ago
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.
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.
(1)
Pavan Kumar said:
2 years ago
The value of √3 is 1.732. By applying this, we will get the answer.
(5)
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers