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If ‘a’ and ‘b’ are distinct positive integers and the quadratic equations
(a−1)x2−a2+2x+a2+2a=0 and (b−1)x2−b2+2x+b2+2b=0 have a common root.
find a²+b²?
(a−1)x2−a2+2x+a2+2a=0 and (b−1)x2−b2+2x+b2+2b=0 have a common root.
find a²+b²?
Most Upvoted Answer
If ‘a’ and ‘b’ are distinct positive integers and the quadratic equati...
Solution:
Given Quadratic Equations:
- Equation 1: (a−1)x^2−a^2+2x+a^2+2a=0
- Equation 2: (b−1)x^2−b^2+2x+b^2+2b=0
Common Root:
- Let the common root of the two equations be 'r'.
- Substitute 'r' in both equations and equate them to find the value of 'a' and 'b'.
Finding a and b:
- Substitute 'r' in Equation 1 and Equation 2:
- (a−1)r^2−a^2+2r+a^2+2a=0
- (b−1)r^2−b^2+2r+b^2+2b=0
- Since 'r' is a common root, the two equations are equal:
- (a−1)r^2−a^2+2r+a^2+2a = (b−1)r^2−b^2+2r+b^2+2b
- Solving the above equation, we get a = b+2.
Calculating a² + b²:
- Substitute a = b+2 in a² + b²:
- a² + b² = (b+2)² + b² = b² + 4b + 4 + b² = 2b² + 4b + 4
Final Answer:
- a² + b² = 2b² + 4b + 4
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If ‘a’ and ‘b’ are distinct positive integers and the quadratic equations (a−1)x2−a2+2x+a2+2a=0 and (b−1)x2−b2+2x+b2+2b=0 have a common root. find a²+b²?
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If ‘a’ and ‘b’ are distinct positive integers and the quadratic equations (a−1)x2−a2+2x+a2+2a=0 and (b−1)x2−b2+2x+b2+2b=0 have a common root. find a²+b²? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If ‘a’ and ‘b’ are distinct positive integers and the quadratic equations (a−1)x2−a2+2x+a2+2a=0 and (b−1)x2−b2+2x+b2+2b=0 have a common root. find a²+b²? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ‘a’ and ‘b’ are distinct positive integers and the quadratic equations (a−1)x2−a2+2x+a2+2a=0 and (b−1)x2−b2+2x+b2+2b=0 have a common root. find a²+b²?.
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