IF (a ka square b ka square c ka square)=250 and ab bc can=3,then a b ...
Given Information:
- (a2 + b2 + c2) = 250
- (ab + bc + ca) = 3
Objective:
To find the values of a, b, and c.
Explanation:
Let's solve the given equations step by step:
Solving Equation 1:
We are given that (a2 + b2 + c2) = 250.
Therefore, a2 + b2 + c2 = 250.
Solving Equation 2:
We are given that (ab + bc + ca) = 3.
Let's square both sides of the equation to eliminate the square root:
(ab + bc + ca)2 = 32
a2b2 + b2c2 + c2a2 + 2ab2c + 2abc2 + 2a2bc = 9
Combining Equations:
We can substitute the values of a2 + b2 + c2 and ab + bc + ca from the given equations into the equation a2b2 + b2c2 + c2a2 + 2ab2c + 2abc2 + 2a2bc = 9.
Substituting the values, we get:
250 + 2ab2c + 2abc2 + 2a2bc = 9
2ab2c + 2abc2 + 2a2bc = 9 - 250
2ab2c + 2abc2 + 2a2bc = -241
Summary:
From the above equation, we have three variables a, b, and c. To find their specific values, we need additional information or equations.