root 13-a root10 = root 8 +root 5
√(13-a) √10 = √8 + √5
√(18-a) = (√8+√5)/√10
18-a = (√8+√5)^2/10
a = 18 - (13+4√10)/10
To solve the equation sqrt(13) - a*sqrt(10) = sqrt(8) + sqrt(5), we can follow these steps:
Step 1: Simplify the equation by moving all square roots to one side and all constants to the other side.
sqrt(13) - sqrt(8) = a*sqrt(10) + sqrt(5)
Step 2: Combine like terms if possible. In this case, there are no like terms to combine.
Step 3: Isolate the variable term on one side by moving the constant term to the other side.
sqrt(13) - sqrt(8) - sqrt(5) = a*sqrt(10)
Step 4: Divide both sides of the equation by sqrt(10) to solve for 'a'.
(a*sqrt(10)) / sqrt(10) = (sqrt(13) - sqrt(8) - sqrt(5)) / sqrt(10)
Simplifying the left side and rationalizing the denominator on the right side:
a = (sqrt(13) - sqrt(8) - sqrt(5)) / sqrt(10)
Now, this represents the value of 'a' that satisfies the equation.
To solve the given equation, we need to isolate the variable "a". Let's break it down step by step:
Step 1: Simplify the equation
First, simplify both sides of the equation by evaluating the square roots.
√13 - a√10 = √8 + √5
Step 2: Move square root terms
Next, move the square root terms to one side of the equation and the "a" term to the other side. Let's move the square root terms to the right side:
-a√10 = √8 + √5 - √13
Step 3: Combine square root terms
Now, combine the square root terms on the right side of the equation. We can't simplify it any further at this point.
-a√10 = √8 + √5 - √13
Step 4: Divide by -√10
To isolate "a", divide both sides of the equation by -√10:
-a√10 / -√10 = (√8 + √5 - √13) / -√10
This gives us:
a = (-√8 - √5 + √13) / √10
Therefore, the value of "a" that satisfies the given equation is (-√8 - √5 + √13) / √10.