For all real numbers a and b, 2a • b = a2 + b2
Is this true or false
False
a=1, b=2=>4=5 false
I confused myself I studied about it and I got it thanks.
TY
To determine if the statement is true or false, we can use counterexamples. A counterexample is a specific example or set of values that satisfy the given conditions and produce a result that does not match the given equation.
In this case, we can find a counterexample by choosing specific values for a and b that make the equation false. The given equation is:
2a • b = a^2 + b^2
Let's try a = 1 and b = 2:
2(1) • 2 = (1^2) + (2^2)
2 • 2 = 1 + 4
4 = 5
Since 4 does not equal 5, we have found a counterexample where the equation does not hold true. Therefore, the statement is false.
a ^ 2 + b ^ 2 = a ^ 2 + 2 a * b + b ^ 2
2 a * b = a ^ 2 + b ^ 2
2 a * b = a ^ 2 + 2 a * b + b ^ 2 Subtract 2 a * b to both sides
2 a * b - 2 a * b = a ^ 2 + 2 a * b + b ^ 2 - 2 a * b
0 = a ^ 2 + b ^ 2 Subtract a ^ 2 to both sides
0 - a ^ 2 = a ^ 2 + b ^ 2 -a ^ 2
- a ^ 2 = b ^ 2
Negative square of a ^ 2 can't be identic with positive b ^ 2.
Obviously false.
This is true only if a = b becouse :
If a = b
2 a * b = a ^ 2 + b ^ 2
2 a * a = a ^ 2 + a ^ 2
2 a ^ 2 = 2 a ^ 2
But in this case a and b is not different numbers.
Answer:
False