How to Solve Radical Equations Using Conguate Radicals

In this video we explained how to solve radical equations using conguates of this radicals.
We mentioned Conjugate Surds : • Conjugate Surds : How ...

[@ManjulaMathew-wb3zn]

Another method.
Let the two radicals be an and b respectively. Then a-b=2 and a^2-b^2=12. Or (a+b)(a-b)=12.
Substituting and solving you get a=4
Substituting in the first radical for a you get x value as 9.
Could do it in the head.

[@demojmathsandsciencetutors]

Very good!
This is one thing I always love to see in mathematics. Many ways to solve a problem

[@MathEducation100M]

Nice sol

[@demojmathsandsciencetutors]

Thank you

[@walterwen2975]

How to Solve Radical Equations: √(x + 7) - √(x - 5) = 2; x = ?
First method:
√(x + 7) - √(x - 5) = 2 = 4 - 2 = √16 - √4 = √(9 + 7) - √(9 - 5); x = 9
Second method:
√(x + 7) = √(x - 5) + 2, x + 7 = [√(x - 5) + 2]² = x - 5 + 4√(x - 5) + 4, 4√(x - 5) = 8
√(x - 5) = 2, x - 5 = 2² = 4; x = 9
Answer check:
x = 9, √(x + 7) - √(x - 5) = 2; Confirmed in First method
Final answer:
x = 9

[@demojmathsandsciencetutors]

This is great. I like ur second approach. It is generic and highly intuitive.

[@user-nd7th3hy4l]

X=9

[@demojmathsandsciencetutors]

Great