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Lera25 [3.4K]
3 years ago
7

At which approximate x-value are these two equations equal y = √1 - x^2 y = 2x - 1

Mathematics
1 answer:
maks197457 [2]3 years ago
8 0

Answer:

Given the equations:

y = \sqrt{1-x^2}           ....[1]

y = 2x-1                  .....[2]

Taking square both sides in [1]  we have;

y^2 = 1-x^2               ....[3]

Substitute the equation [2] into [3] we have;

(2x-1)^2 = 1-x^2

Using identity rule: (a-b)^2 = a^-2ab+b^2

then;

4x^2-4x+1 = 1-x^2

Add x^2 both sides we have;

5x^2-4x+1 = 1

Subtract 1 from both sides we have;

5x^2-4x=0

⇒x(5x-4) = 0

By zero product property we have;

x = 0 and 5x-4 = 0

⇒x= 0 and x = \frac{4}{5} = 0.8

For x = 0,

y=\sqrt{1-0} = 1

y = 2(0)-1 = -1

Since, the value of x = 0 doesn't satisfy the equations.

Therefore, the values of x is 0.8

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