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ten less than a number is the same as the square root of seven times the same number greater than eight . what is the number.

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MARIHANI99IN

Let x be the number

[tex]x - 10 = \sqrt{7x + 8} \\ {(x - 10)}^{2} = { \sqrt{7x + 8} }^{2} \\ {x}^{2} - 20x + 100 = 7x + 8 \\ {x}^{2} - 20x + 100 - 7x - 8 = 0 \\ {x}^{2} - 27x + 92 = 0 \\ (x - 23)(x - 4) = 0 \\ \\ x - 23 = 0 \\ x = 23 \\ \\ x - 4 = 0 \\ x = 4[/tex]

Therefore the number is 23 or 4.

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