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If x+2y=10, xy=15 then find the value of x^3+8y^3?
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If x+2y=10, xy=15 then find the value of x^3+8y^3?
Solution:
Given equations: x + 2y = 10, xy = 15
Finding the values of x and y:
- Let's solve the given equations simultaneously.
- From the first equation, we can express x in terms of y: x = 10 - 2y
- Substitute this value of x in the second equation: (10 - 2y)y = 15
- Simplify the equation: 10y - 2y^2 = 15
- Rearrange the terms: 2y^2 - 10y + 15 = 0
- Solve the quadratic equation to find the values of y
- y = 3 or y = 5
- Substitute the values of y back to find x
- For y = 3, x = 10 - 2(3) = 4
- For y = 5, x = 10 - 2(5) = 0
Finding x^3 + 8y^3:
- Plug in the values of x and y into the expression x^3 + 8y^3
- For y = 3, x = 4: x^3 + 8y^3 = 4^3 + 8(3)^3 = 64 + 216 = 280
- For y = 5, x = 0: x^3 + 8y^3 = 0^3 + 8(5)^3 = 0 + 1000 = 1000
Conclusion:
- The values of x^3 + 8y^3 are 280 and 1000 for y = 3 and y = 5, respectively.
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If x+2y=10, xy=15 then find the value of x^3+8y^3? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x+2y=10, xy=15 then find the value of x^3+8y^3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x+2y=10, xy=15 then find the value of x^3+8y^3?.
If x+2y=10, xy=15 then find the value of x^3+8y^3? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x+2y=10, xy=15 then find the value of x^3+8y^3? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x+2y=10, xy=15 then find the value of x^3+8y^3?.
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