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Question Number 57175 by Tinkutara last updated on 31/Mar/19

Commented by Tinkutara last updated on 31/Mar/19

Please help in all the 3 questions!

Commented by mr W last updated on 31/Mar/19

$$Q11:$$$$\mid a+b\frac{y}{x}\mid \mid x\mid +\mid b\frac{x}{y}+a\mid \mid y\mid =\mid x\mid +\mid y\mid$$$$or$$$$\mid a\frac{x}{y}+b\mid \mid y\mid +\mid b+a\frac{y}{x}\mid \mid x\mid =\mid x\mid +\mid y\mid$$$$$$$$b=0$$$$a=\pm 1$$$$or$$$$a=0$$$$b=\pm 1$$$$$$$$\Rightarrow \mid a\mid +\mid b\mid =1$$

Commented by Tinkutara last updated on 31/Mar/19

But Sir how to solve if a and b are both other than 0?

Commented by mr W last updated on 31/Mar/19

$$thereisnosolutionwitha\ne 0andb\ne 0.$$$$sincexandycanbeofanyvalues,$$$$wewillgeta+b=\pm 1anda-b=\pm 1,$$$$therefore(a=\pm 1andb=0)or(a=0and$$$$b=\pm 1).nootherpossibility.$$

Commented by Tinkutara last updated on 02/Apr/19

Thank you Sir!

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