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Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.?
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Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, ...
Proof by Contradiction:
Assume that the given equation has a real root, say x = k.
Substituting k for x, we get:
(a² b²) k² + 2(ac bd) k + (c² d²) = 0
Using the quadratic formula, we get:
k = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
k = (-2(ac bd) ± √((2(ac bd))² - 4(a² b²)(c² d²))) / 2(a² b²)
Simplifying this equation, we get:
k = (-1/ab) (ac bd ± √((ad - bc)²))
Since ad ≠ bc, we have:
(ad - bc)² > 0
Therefore, √((ad - bc)²) > 0
So, k cannot be real, as:
k = (-1/ab) (ac bd ± √((ad - bc)²))
and √((ad - bc)²) > 0
Hence, the given equation has no real root if ad ≠ bc.
Assume that the given equation has a real root, say x = k.
Substituting k for x, we get:
(a² b²) k² + 2(ac bd) k + (c² d²) = 0
Using the quadratic formula, we get:
k = (-b ± √(b² - 4ac)) / 2a
Substituting the values of a, b, and c, we get:
k = (-2(ac bd) ± √((2(ac bd))² - 4(a² b²)(c² d²))) / 2(a² b²)
Simplifying this equation, we get:
k = (-1/ab) (ac bd ± √((ad - bc)²))
Since ad ≠ bc, we have:
(ad - bc)² > 0
Therefore, √((ad - bc)²) > 0
So, k cannot be real, as:
k = (-1/ab) (ac bd ± √((ad - bc)²))
and √((ad - bc)²) > 0
Hence, the given equation has no real root if ad ≠ bc.
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Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.?
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Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.?.
Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve that Show that (a² b²)x² 2(ac bd) x (c² d²) =0has no real root, if ad=not equal to bc.?.
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