SOLUTION: can you help me here? a number is increased by the square root of this result is less than the square root of half the number is 3. Find the number.
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Question 931131: can you help me here? a number is increased by the square root of this result is less than the square root of half the number is 3. Find the number.
Answer by ptfile(81) (Show Source): You can put this solution on YOUR website!
Let x = the number
A number is increased by the square root of this result is less than the square root of half the number is 3.
√x-√(x/2)=3
√ x=√(x/2)+3
(√x)^2=(√(x/2)+3)^2
x=x/2+6√(x/2)+9
0=-x+x/2+6√(x/2)+9
0=-x/2+(6√(x/2))(√(2/2)+9
0=-x/2+6√(2x/2)/2+18/2
0=-x+6√2x+18
(x-18)^2=(6√2x)^2
x^2-36x+324=72x
x^2-36x+324-72x=0
x^2-108x+324=0
Use Quadratic formula to solve for x
x = 104.91168824543142175686079407155 or 105
or
x = 3.08831175456857824313920592845 or 3
Substitute x for 105
√(105)-√((105)/2)= 3
10 - 7 = 3
3 = 3
Substitute x for 3
√(3)-√((3)/2)= 3
2 - 1 = 3
1 = 3
The number is 105.
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