Airforce X Y / Indian Navy SSR Exam > Airforce X Y / Indian Navy SSR Questions > Ifx − y = 2, xy = 24, then the value of...
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If x − y = 2, xy = 24, then the value of (x2 + y2) is:
- a)25
- b)36
- c)63
- d)52
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Ifx − y = 2, xy = 24, then the value of(x2+ y2)is:a)25b)36c)63d)...
Given,
x − y = 2 and xy = 24
By squaring, we get
(x − y)2 = 22
⇒ x2 + y2 − 2xy = 4
⇒ x2 + y2 − 2 × 24 = 4
⇒ x2 + y2 = 4 + 48
⇒ x2 + y2 = 52
x − y = 2 and xy = 24
By squaring, we get
(x − y)2 = 22
⇒ x2 + y2 − 2xy = 4
⇒ x2 + y2 − 2 × 24 = 4
⇒ x2 + y2 = 4 + 48
⇒ x2 + y2 = 52
Most Upvoted Answer
Ifx − y = 2, xy = 24, then the value of(x2+ y2)is:a)25b)36c)63d)...
Given Equations
We start with the equations:
- Ifx - y = 2
- xy = 24
Finding x and y
1. From the first equation, express x in terms of y:
- x = y + 2
2. Substitute x in the second equation:
- (y + 2)y = 24
- y^2 + 2y - 24 = 0
3. Factor the quadratic equation:
- (y + 6)(y - 4) = 0
4. Solve for y:
- y = -6 (not valid since we need positive values)
- y = 4
5. Substitute y back to find x:
- x = 4 + 2 = 6
Calculating x² + y²
To find x² + y², we can use the identity:
- x² + y² = (x - y)² + 2xy
1. Calculate (x - y)²:
- x - y = 2
- (x - y)² = 2² = 4
2. Calculate 2xy:
- 2xy = 2 * 24 = 48
3. Now, combine the results:
- x² + y² = 4 + 48 = 52
Conclusion
Thus, the value of x² + y² is 52, confirming that the correct answer is option 'D'.
We start with the equations:
- Ifx - y = 2
- xy = 24
Finding x and y
1. From the first equation, express x in terms of y:
- x = y + 2
2. Substitute x in the second equation:
- (y + 2)y = 24
- y^2 + 2y - 24 = 0
3. Factor the quadratic equation:
- (y + 6)(y - 4) = 0
4. Solve for y:
- y = -6 (not valid since we need positive values)
- y = 4
5. Substitute y back to find x:
- x = 4 + 2 = 6
Calculating x² + y²
To find x² + y², we can use the identity:
- x² + y² = (x - y)² + 2xy
1. Calculate (x - y)²:
- x - y = 2
- (x - y)² = 2² = 4
2. Calculate 2xy:
- 2xy = 2 * 24 = 48
3. Now, combine the results:
- x² + y² = 4 + 48 = 52
Conclusion
Thus, the value of x² + y² is 52, confirming that the correct answer is option 'D'.
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Community Answer
Ifx − y = 2, xy = 24, then the value of(x2+ y2)is:a)25b)36c)63d)...
Given,
x − y = 2 and xy = 24
By squaring, we get
(x − y)2 = 22
⇒ x2 + y2 − 2xy = 4
⇒ x2 + y2 − 2 × 24 = 4
⇒ x2 + y2 = 4 + 48
⇒ x2 + y2 = 52
x − y = 2 and xy = 24
By squaring, we get
(x − y)2 = 22
⇒ x2 + y2 − 2xy = 4
⇒ x2 + y2 − 2 × 24 = 4
⇒ x2 + y2 = 4 + 48
⇒ x2 + y2 = 52
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Ifx − y = 2, xy = 24, then the value of(x2+ y2)is:a)25b)36c)63d)52Correct answer is option 'D'. Can you explain this answer?
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