is the following equations lineara in x
2 square root x+5=10
and
x+1/x=1
no, yes.
what about x-3= x^2
To determine if the given equations are linear in x, we need to check if the highest power of x is 1 and if there are no other terms involving x raised to a higher power. Let's analyze each equation separately:
1) Equation: 2√x + 5 = 10
To check if it is linear in x, we need to simplify the equation and see if the highest power of x is 1.
Subtracting 5 from both sides, we get:
2√x = 5
Next, let's square both sides to eliminate the square root:
(2√x)² = 5²
4x = 25
From this step, we can see that the highest power of x is 1 (x^1). So, this equation is linear in x.
2) Equation: x + 1/x = 1
To determine if it is linear, let's simplify and analyze.
Multiplying both sides by x, we get:
x² + 1 = x
Rearranging the terms:
x² - x + 1 = 0
We can observe that the highest power of x is 2 (x^2), which is higher than 1. Hence, this equation is not linear in x.
In conclusion, the first equation, 2√x + 5 = 10, is linear in x, while the second equation, x + 1/x = 1, is not linear in x.