Find the real solutions of the equati √7x+1 - √x-5 = 6

Mathematics

1 answer:

Juliette [100K]1 year ago

5 0

The solution of this equation is x = 5 and x = 9.

<h3>What is the solution?</h3>

Let us recall that what we have here is a radical equation as follows;

√7x+1 - √x-5 = 6

When we isolate we have';

√7x+1 = √x-5+6

Taking the square of both sides;

(√7x+1)^2 = (√x-5+6)^2

Hence;

7x+1 = x-5+36+12√x-5

-12√x-5 = -7x-1+x-5+36

12√x-5 = 6x-30

Raising this equation to power 2

144x-720 = 36x^2-360x+900

When we rearrange we obtain;

36x2 - 504x + 1620 = 0

Hence;

x = 5 and x = 9

Learn more about radical equation:brainly.com/question/8606917

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Confirming if t=0 satisfy the other equation

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Finding the tangent vector at t=0

$\frac{dx}{dt}=-2te^{-2t} cos4t + e^{-2t}(-4sin4t)=-2(0)e^{-2(0)} cos4(0) + e^{-2(0)}(-4sin4(0))=0\\\\ \frac{dy}{dt} =-2te^{-2t} sin4t + e^{-2t}(4cos4t)=-2(0)e^{-2(0)} sin4(0)+ e^{-2(0)(4cos4(0)) }= 1\\\\\frac{dz}{dt} = -2te^{-2t} = -2(0)e^{-2(0)} = 0$