Simplifying the Algebraic Expression
To find the value of the given expression, we can use algebraic identities. Let $a = 74$ and $b = 47$. The expression becomes:
$ \frac{(a + b)^2 + (a - b)^2}{a^2 + b^2} $Applying Algebraic Identities
We know the following algebraic identities:
- $(a + b)^2 = a^2 + 2ab + b^2$
- $(a - b)^2 = a^2 - 2ab + b^2$
Substitute these into the numerator:
$ (a + b)^2 + (a - b)^2 = (a^2 + 2ab + b^2) + (a^2 - 2ab + b^2) $Combine like terms:
$ = a^2 + a^2 + 2ab - 2ab + b^2 + b^2 $ $ = 2a^2 + 2b^2 $ $ = 2(a^2 + b^2) $Final Simplification
Now substitute this simplified numerator back into the original expression:
$ \frac{2(a^2 + b^2)}{a^2 + b^2} $Cancel out the common term $a^2 + b^2$ from the numerator and denominator:
$ = 2 $Therefore, the value of the expression $\frac{(74 + 47)^2 + (74 - 47)^2}{74^2 + 47^2}$ is 2.
Final Answer: The final answer is 2
Similar Questions
- If $a + b + c = 10$ and $ab + bc + ca = 31$, find the value of $a^2 + b^2 + c^2$
If $a + b + c = 0$, then find the value of $\frac{(a^2+b^2+c^2)^2}{a^2b^2+b^2c^2+c^2a^2}$
- If $x^4 + \frac{1}{x^4} = 322$, then $x^3 - \frac{1}{x^3} = ?$
- If $(x + \frac{1}{x}) = 7$, then $(x - \frac{1}{x})$ is equal to:
- If $x + y + z = 0$, then the value of $\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$ is:
- What is the value of the following expression:
$(1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x)$ - If $a + b + c = 17$, $abc = 168$, and $ab + bc + ca = 94$, then $a^3 + b^3 + c^3 = ?$
- If $a = \frac{b^2}{b - a}$, then the value of $a^3 + b^3$ is:
- If $ab = 10$ and $a^{2} + b^{2} = 29$, then $(a - b)^{2} = ?$
- If $\left(\text{a}^2 + \frac{1}{\text{a}^2}\right) = 18$ then find $\left(\text{a} - \frac{1}{\text{a}}\right)$
Important Questions from Identities
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
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?
If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of \(\frac{abc}{5}\) is:
(999) 2- 2 2=
