Algebraic Identity Solution
We need to find the value of $(a - b)^{2}$ given the equations $ab = 10$ and $a^{2} + b^{2} = 29$.
Using the Algebraic Identity
Recall the algebraic identity for the square of a difference:
$ (a - b)^{2} = a^{2} - 2ab + b^{2} $
This can be rearranged as:
$ (a - b)^{2} = (a^{2} + b^{2}) - 2ab $
Substituting Given Values
We are given:
- $a^{2} + b^{2} = 29$
- $ab = 10$
Substitute these values into the identity:
$ (a - b)^{2} = (29) - 2(10) $
Calculating the Result
Perform the subtraction:
$ (a - b)^{2} = 29 - 20 $
$ (a - b)^{2} = 9 $
Therefore, the value of $(a - b)^{2}$ is 9.
Similar Questions
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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?
