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If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is?
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If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is?
Answer:
Given: p:q is the sub duplicate ratio of p-x^:q-x^
To find: x^
Solution:
We know that the sub duplicate ratio formula is,
(a-b):(a+b) = sqrt(a):sqrt(b)
Using this formula,
p:q = sqrt(p-x^):sqrt(q-x^)
Squaring both sides of the equation, we get,
(p:q)^2 = (sqrt(p-x^):sqrt(q-x^))^2
p^2:q^2 = (p-x^):(q-x^)
Cross-multiplying the ratio, we get,
p^2(q-x^) = q^2(p-x^)
Expanding the equation, we get,
p^2q - p^2x^ = q^2p - q^2x^
Transposing the terms, we get,
p^2x^ - q^2x^ = q^2p - p^2q
Factorizing the equation, we get,
x^ (p^2 - q^2) = q^2p - p^2q
Dividing both sides by (p^2 - q^2), we get,
x^ = (q^2p - p^2q)/(p^2 - q^2)
Therefore, the value of x^ is (q^2p - p^2q)/(p^2 - q^2).
Conclusion:
Hence, the solution to the given problem is x^ = (q^2p - p^2q)/(p^2 - q^2).
Given: p:q is the sub duplicate ratio of p-x^:q-x^
To find: x^
Solution:
We know that the sub duplicate ratio formula is,
(a-b):(a+b) = sqrt(a):sqrt(b)
Using this formula,
p:q = sqrt(p-x^):sqrt(q-x^)
Squaring both sides of the equation, we get,
(p:q)^2 = (sqrt(p-x^):sqrt(q-x^))^2
p^2:q^2 = (p-x^):(q-x^)
Cross-multiplying the ratio, we get,
p^2(q-x^) = q^2(p-x^)
Expanding the equation, we get,
p^2q - p^2x^ = q^2p - q^2x^
Transposing the terms, we get,
p^2x^ - q^2x^ = q^2p - p^2q
Factorizing the equation, we get,
x^ (p^2 - q^2) = q^2p - p^2q
Dividing both sides by (p^2 - q^2), we get,
x^ = (q^2p - p^2q)/(p^2 - q^2)
Therefore, the value of x^ is (q^2p - p^2q)/(p^2 - q^2).
Conclusion:
Hence, the solution to the given problem is x^ = (q^2p - p^2q)/(p^2 - q^2).
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If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is?
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If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is?.
If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p:q is the sub duplicate ratio of p-x^:q-x^ then x^ is?.
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