Question

Вычислите (181^2-61^2)/(319^2-209^2) Это ДРОБЬ!!

Answer 1

=  (181-61)(181+61)     = 120 * 242 =  1 2 * 121    =  11  = 1/2 = 0,5
   (319-209)(319+209)      110*528      11 * 264         22

Answer 2

Calculating the Fraction

To calculate the value of the given fraction, we can use the formula for the difference of squares, which states that \(a^2 - b^2 = (a + b)(a - b)\).

So, for the given expression \(\frac{{181^2 - 61^2}}{{319^2 - 209^2}}\), we can apply the difference of squares formula to simplify the numerator and the denominator.

Simplifying the Numerator and Denominator

Using the difference of squares formula: - \(181^2 - 61^2 = (181 + 61)(181 - 61)\) - \(319^2 - 209^2 = (319 + 209)(319 - 209)\)

Applying the Formula

Now, let's apply the formula to simplify the expression: - \(181^2 - 61^2 = 242 \times 120\) - \(319^2 - 209^2 = 528 \times 110\)

Calculating the Fraction

Substituting the simplified values back into the original expression: \(\frac{{181^2 - 61^2}}{{319^2 - 209^2}} = \frac{{242 \times 120}}{{528 \times 110}}\)

Final Calculation

Now, we can calculate the value of the fraction: \(\frac{{242 \times 120}}{{528 \times 110}} = \frac{{29040}}{{58080}} = \frac{{485}}{{968}}\)

So, the value of the given fraction \(\frac{{181^2 - 61^2}}{{319^2 - 209^2}}\) is \(\frac{{485}}{{968}}\).