Question

What is the solution to the equation


`√(4t + 5) = 3 - √(t + 5)`
● x= -1, x=11
● x= -1
● x= 11
● no solution

Answer 1

-1

Explanation:

:)

Answer 2

`√(4t+5)=3-√(t+5)\\\\D:4t+5\geq0\ \wedge\ t+5\geq0\ \wedge\ √(t+5)\leq3\\\\t\geq-(5)/(4)\ \wedge\ t\geq-5\ \wedge\ t\leq6`

therefore

`D:x\in\left< -(5)/(4);\ 6\right>`


`√(4t+5)=3-√(t+5)\ \ \ |^2\\\\(√(4t+5))^2=(3-√(t+5))^2\ \ \ |use:(a-b)^2=a^2-2ab+b^2\\\\4t+5=3^2-2\cdot3\cdot√(t+5)+(√(t+5))^2\\\\4t+5=9-6√(t+5)+t+5\ \ \ \ |-t\\\\3t+5=14-6√(t+5)\ \ \ \ |-14\\\\3t-9=-6√(t+5)\ \ \ \ |change\ signs`

`9-3t=6√(t+5)\ \ \ \ |:3\\\\3-t=2√(t+5)\ \ \ \ |^2\\\\(3-t)^2=(2√(t+5))^2\\\\3^2-2\cdot3\cdot t+t^2=4(t+5)\\\\9-6t+t^2=4t+20\ \ \ |-4t-20\\\\t^2-10t-11=0\\\\t^2+t-11t-11=0\\\\t(t+1)-11(t+1)=0\\\\(t+1)(t-11)=0\iff t+1=0\ \vee\ t-11=0\\\\t=-1\in D\ \vee\ t=11\\otin D`
Answer: t = -1.