the square root of 5 less than 6 times a certain number is divided by the number and the quotient is 1.Find the number
√(6x-5)/x = 1
6x-5 = x^2
x^2-6x+5 = 0
x = 1 or 5
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Let's break down the problem step-by-step:
Step 1: Let's represent the certain number as 'x'.
Step 2: We have the expression "the square root of 5 less than 6 times a certain number". In algebraic terms, this can be written as √(6x - 5).
Step 3: According to the problem, this expression is divided by the number 'x' and the quotient is 1. In equation form, this can be written as:
√(6x - 5) / x = 1
Step 4: To solve this equation, let's square both sides to eliminate the square root:
(√(6x - 5) / x)^2 = 1^2
(6x - 5) / (x^2) = 1
Step 5: Multiply both sides of the equation by x^2 to clear the fraction:
(6x - 5) = x^2
Step 6: Rearrange the equation to get a quadratic equation:
x^2 - 6x + 5 = 0
Step 7: Solve the quadratic equation by factoring or using the quadratic formula:
(x - 5)(x - 1) = 0
Step 8: Set each factor equal to zero and solve for 'x':
x - 5 = 0 or x - 1 = 0
Step 9: Solve for 'x':
x = 5 or x = 1
Therefore, the possible values for the certain number is x = 5 or x = 1.
To find the number, let's break down the given information into steps:
Step 1: Let's assume the certain number as 'x'.
Step 2: We are given that the square root of 5 less than 6 times the certain number is divided by the number, and the quotient is 1. Mathematically, this can be represented as:
(sqrt(6x - 5)) / x = 1
Step 3: To find the number 'x', we can solve the equation by multiplying both sides by 'x'. This gives us:
sqrt(6x - 5) = x
Step 4: Now, we can square both sides of the equation to eliminate the square root:
(6x - 5) = x^2
Step 5: Rearrange the equation to isolate the variable 'x':
x^2 - 6x + 5 = 0
Step 6: Now, we can solve this quadratic equation by factoring or using the quadratic formula. In this case, we can factor the equation as:
(x - 5)(x - 1) = 0
Step 7: Setting each factor equal to zero, we get two possible solutions:
x - 5 = 0 -> x = 5
x - 1 = 0 -> x = 1
Step 8: Therefore, the certain number can be either 5 or 1, as both values of 'x' satisfy the given conditions.
So, the number can be 5 or 1.