InterviewSolution
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InterviewSolution
| 1. |
x/a+y/b=2ax-by=a2-b2 |
| Answer» {tex}\\frac { x } { a } + \\frac { y } { b } = 2{/tex}{tex}\\frac { b x + a y } { a b } = 2{/tex}{tex}bx + ay = 2ab{/tex}........(i){tex}ax - by = (a^2\xa0- b^2){/tex}...(ii)Multiplying (i) by b and (ii) by a{tex}b^2x + bay = 2ab^2{/tex}.............(iii){tex}a^2x - bay = a(a^2\xa0- b^2){/tex}........(iv)Adding (iii) and (iv),we get{tex}b^2x + a^2x =\xa02ab^2\xa0+ a^3\xa0- ab^2{/tex}{tex}x(b^2\xa0+ a^2) = 2ab^2\xa0+ a^3\xa0- ab^2{/tex}{tex}x(b^2\xa0+ a^2)\xa0=\xa0ab^2\xa0+ a^3{/tex}{tex}x(b^2\xa0+ a^2)\xa0=a(b^2\xa0+ a^2){/tex}{tex}x = \\frac { a \\left( b ^ { 2 } + a ^ { 2 } \\right) } { \\left( b ^ { 2 } + a ^ { 2 } \\right) } = a{/tex}Putting x = a in (i),we get{tex}b \\times a + a y = 2 a b{/tex}{tex}a y = 2 a b - a b \\Rightarrow a y = a b{/tex}\xa0or y = b{tex}\\therefore{/tex}\xa0solution is x = a, y = b | |