3n=squareroot of 10n-1
And
Y=squareroot of 7y-10
Help would be greatly appreciated!
which of the following do you mean
3n = √(10n) - 1
3n = √(10n-1)
3n = √10 n - 1
The way you typed it , it would be the last one, but somehow I doubt that is what you meant.
Please clarify the above, as well as your second question in this post.
Sorry yes it is the first one
The second would be that same way
then
3n = √(10n) - 1
3n + 1 = √(10n)
square both sides
9n^2 + 6n + 1 = 10n
9n^2 -4n + 1 = 0
This quadratic has no real roots.
Are you sure you did not mean
3n = √(10n-1) ????, because then after squaring
9n^2 = 10n - 1
9n^2 - 10n + 1 = 0
(n-1)(9n-1) = 0
n = 1 or n = 1/9
if n=1,
LS = 3
RS = √(10-1) = √9 = 3 = LS
if n=1/9
LS = 3(1/9) = 1/3
RS = √(10/9 - 1)
= √(1/9) = √1/√9 = 1/3 =
so n = 1 or n = 1/9
Do the second the same way after seeing it as
y = √(7y-10)
( I can see two "nice" answers)
Yep you were right. Thank you so much. I really appreciate it.
Sure! Let's solve each equation step by step.
1) Starting with the equation 3n = √(10n - 1):
To isolate the variable n, we need to eliminate the square root on the right side. To do this, we square both sides of the equation:
(3n)^2 = (√(10n - 1))^2
9n^2 = 10n - 1
Rearrange the equation to bring all terms to one side:
9n^2 - 10n + 1 = 0
This is a quadratic equation. To solve it, we can either factorize or use the quadratic formula. In this case, factoring is not easy, so let's use the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 9, b = -10, and c = 1:
n = (-(-10) ± √((-10)^2 - 4*9*1)) / (2*9)
n = (10 ± √(100 - 36)) / 18
n = (10 ± √64) / 18
n = (10 ± 8) / 18
This gives us two possible solutions:
n = (10 + 8) / 18 = 18 / 18 = 1
n = (10 - 8) / 18 = 2 / 18 = 1/9
So, the equation 3n = √(10n - 1) has two solutions: n = 1 and n = 1/9.
2) Moving on to the equation y = √(7y - 10):
Similarly, we need to eliminate the square root on the right side by squaring both sides:
y^2 = (√(7y - 10))^2
y^2 = 7y - 10
Rearranging the equation to one side:
y^2 - 7y + 10 = 0
This is again a quadratic equation, but this time it can be factored easily:
(y - 5)(y - 2) = 0
Setting each factor equal to zero:
y - 5 = 0 or y - 2 = 0
y = 5 or y = 2
So, the equation y = √(7y - 10) has two solutions: y = 5 and y = 2.
I hope this helps! Let me know if you have any further questions.