five times the square root of 1 less than a number is equal to 3 more than the n...

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five times the square root of 1 less than a number is equal to 3 more than the number find the number

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✏️NUMBER

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Problem: Five times the square root of 1 less than a number is equal to 3 more than the number. Find the number.

Solution: Let x be the number then solve it.

$5 \sqrt{x - 1} = x + 3$

$(5 \sqrt{x - 1} )^{2} = (x + 3)^{2}$

$25(x - 1) = (x + 3)(x + 3)$

$25x - 25 = {x}^{2} + 6x + 9$

$\text - {x}^{2} + 25x - 6x - 25 - 9 = 0$

$\text - {x}^{2} + 19x - 34 = 0$

${x}^{2} - 19x + 34 = 0$

- Solve the quadratic equation by factoring.

$(x - 17)(x - 2) = 0$

$x - 17 = 0 \: \: \: \: ; \: \: \: \: x - 2 = 0$

$x = 17 \: \: \: \: ; \: \: \: \: x = 2$

- Therefore, the numbers are:

$\large \rm Numbers = \boxed{ \rm \green{ \: 17 \: and \: 2 \: }}$

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✏️NUMBER

===============================

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Add an Answer

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