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Question Number 133423 by mathlove last updated on 22/Feb/21

Commented by liki last updated on 24/Feb/21

$$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{and}\mathrm{y}?$$

Commented by MJS_new last updated on 24/Feb/21

I gave the answer 2 days ago. What's the problem?

Commented by liki last updated on 24/Feb/21

$$\mathrm{sory}\mathrm{sir}\mathrm{i}\mathrm{did}\mathrm{not}\mathrm{see}\mathrm{the}\mathrm{answer}$$

Commented by liki last updated on 24/Feb/21

$$\mathrm{if}\mathrm{possible}\mathrm{sir}\mathrm{tell}\mathrm{me}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{and}\mathrm{y}$$

Answered by MJS_new last updated on 24/Feb/21

$${(2x-6)}^y=1$$$$\left(1\right)r^0=1\mathrm{\forall }r\ne 0\Rightarrow x\in \mathbb{R}\wedge x\ne 3\wedge y=0$$$$\left(2\right)1^r=1\mathrm{\forall }r\in \mathbb{R}\Rightarrow x=\frac{7}{2}\wedge y\in \mathbb{R}$$$$\left(3\right){(-1)}^{2z}=1\mathrm{\forall }z\in \mathbb{Z}\Rightarrow x=\frac{5}{2}\wedge y=2x;z\in \mathbb{Z}$$

Commented by MJS_new last updated on 24/Feb/21

$$\mathrm{we}\mathrm{have}\mathrm{these}\mathrm{three}\mathrm{groups}\mathrm{of}\mathrm{solutions}$$$$\left(1\right)\mathrm{for}y=0\mathrm{we}\mathrm{can}\mathrm{take}\mathrm{any}x\ne 3$$$$\left(2\right)\mathrm{for}x=\frac{7}{2}\mathrm{we}\mathrm{can}\mathrm{take}\mathrm{any}y\in \mathbb{R}$$$$\left(3\right)\mathrm{for}x=\frac{5}{2}\mathrm{we}\mathrm{can}\mathrm{take}\mathrm{any}\mathrm{even}y\in \mathbb{Z}$$

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