b. Solve this radical equation: sqrt{3x+2}+sqrt{x+7}=1 . (You need to tell Patricia that simply squaring both sides will not do the trick and explain why. Discuss the method used to solve such equations. Show her how once you set up the equation correctly, it’s simply a quadratic equation that can be solved by straightforward methods.)

Question

b.	Solve this radical equation: sqrt{3x+2}+sqrt{x+7}=1  . (You need to tell Patricia that simply squaring both sides will not do the trick and explain why. Discuss the method used to solve such equations. Show her how once you set up the equation correctly, it’s simply a quadratic equation that can be solved by straightforward methods.)

anonymous · Answer

$$\sqrt{3x+2}+\sqrt{x+7}=1$$

anonymous · Answer

$$\sqrt{3x+2}+\sqrt{x+7}=1$$

zepdrix · Answer

Mmmm I dunno :(
@campbell_st @whpalmer4

campbell_st · Answer

well I'd square both sides 

and you'll get 

$$3x + 2 + 2\sqrt{3x +2}\sqrt{x + 7} + x + 7 = 1$$

so 

$$4x + 9 + 2\sqrt{(3x + 2)(x + 7} = 1$$

so 

$$2\sqrt{3x^2 + 23x + 14} = -4x - 8$$

so 

$$\sqrt{3x^2 + 23x + 14} = -2x - 4$$

so prehaps squaring both sides again will give

$$3x^2 + 23x + 14 = 4x^2+ 16x + 16$$

and allow you to solve for x.... that's my best guess..

campbell_st · Answer

so looking at things, there are irrational solutions to the value of x, but I'd say that because of the domain restrictions, then there maybe no solutions.

campbell_st · Answer

perhaps wolfram alpha may be your best bet for a more detailed answer