For all real numbers a and b, 2a • b = a2 + b2
Is this true or false
False
a=1, b=2=>4=5 false
3 answers
I confused myself I studied about it and I got it thanks.
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
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
TY
1 answer