If and , then find the value of the following expression:
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Note: This is a very Basic approach which is expected to be useful for beginners.
We can simply separate this expression into 3 sections:
S1: Finding a 2 + b 2
S2: Finding 4 a b
S3: It is just about solving the expression
So lets begin with: Section 1
To find the values of a 2 + b 2 we use the formula:
( a + b ) 2 + ( a − b ) 2 = 2 ( a 2 + b 2 )
Putting the values of a + b and a − b , we get:
2 ( a 2 + b 2 ) = ( 5 ) 2 + ( 3 ) 2 = 2 5 + 9 = 3 4 or
( a 2 + b 2 ) = 2 ) 3 4 = 17
Section 2
To find the value of 4 a b we use the formula:
( a + b ) 2 − ( a − b ) 2 = 4 a b
** I'm lazy to type. just do the calculations since you know the formula
You are sure to get:
4 a b = 1 6
Section 3
To find the value of 1 6 a b ( a 2 + b 2 ) , we have
1 6 a b ( a 2 + b 2 ) = 4 ( 4 a b ) ( a 2 + b 2 )
Using the result in S1 and S2
= 4 (16) (17)
= 1088