Calculate \(a^2 + b^2\) Using Given Sum and Product
This problem requires finding the value of \(a^2 + b^2\) given the values of \(a + b\) and \(ab\). We can use a standard algebraic identity to solve this efficiently.
Using Algebraic Identity
The relevant algebraic identity is:
\((a+b)^2 = a^2 + 2ab + b^2\)
We need to find \(a^2 + b^2\). Rearranging the identity, we get:
\(a^2 + b^2 = (a+b)^2 - 2ab\)
Substituting Given Values
We are given:
- \(a + b = 12\)
- \(ab = 32\)
Substitute these values into the rearranged formula:
\(a^2 + b^2 = (12)^2 - 2(32)\)
Step-by-Step Calculation
- Calculate the square of the sum: \((12)^2 = 144\).
- Calculate twice the product: \(2 \times 32 = 64\).
- Subtract the result from step 2 from the result in step 1: \(144 - 64\).
\(a^2 + b^2 = 144 - 64\)
\(a^2 + b^2 = 80\)
Therefore, the value of \(a^2 + b^2\) is 80.
Similar Questions
- If a + b = 7 and ab = 12, then \(a^2 + b^2\) is equal to:
Important Questions from Identities
If \(2x + { {1} \over 3x}= 5, x ≠ 0\) , then what is the value of \(27x^3+{{1} \over 8x^3}\) ?
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(0.73)^3+(0.31)^3}{(0.73)^2-0.73\times0.31+(0.31)^2}\)
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
