Q1) Solve the following pair of equations by cross-multiplication method a²x+b²y=c² and b²x+a²y=d²

Asked by mkmishra101 | 21st Jun, 2016, 02:31: PM

Expert Answer:

begin mathsize 12px style Begin space by space writing space the space equations space in space the space general space form.
straight a squared straight x plus straight b squared straight y equals straight c squared space becomes space straight a squared straight x plus straight b squared straight y minus straight c squared space equals 0 space and space
straight b squared straight x plus straight a squared straight y equals straight d squared space becomes space straight b squared straight x plus straight a squared straight y minus straight d squared space equals 0
end style
 
begin mathsize 12px style fraction numerator straight x over denominator negative straight b squared straight d squared plus straight a squared straight c squared end fraction equals fraction numerator straight y over denominator negative straight c squared straight b squared plus straight a squared straight d squared end fraction equals fraction numerator 1 over denominator straight a to the power of 4 minus straight b to the power of 4 end fraction
rightwards double arrow straight x equals fraction numerator negative straight b squared straight d squared plus straight a squared straight c squared over denominator straight a to the power of 4 minus straight b to the power of 4 end fraction space and space straight y space equals space fraction numerator negative straight c squared straight b squared plus straight a squared straight d squared over denominator straight a to the power of 4 minus straight b to the power of 4 end fraction
Hence space the space solution space is space straight x equals fraction numerator negative straight b squared straight d squared plus straight a squared straight c squared over denominator straight a to the power of 4 minus straight b to the power of 4 end fraction space and space straight y space equals space fraction numerator negative straight c squared straight b squared plus straight a squared straight d squared over denominator straight a to the power of 4 minus straight b to the power of 4 end fraction. end style

Answered by Rebecca Fernandes | 21st Jun, 2016, 03:39: PM

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