Question

31.10. Докажите, что значение выражения не зависит от перемен- ной а: 4) (17 + a)(17 - a) - (0,6 - a)(a +0,6). ​

Answer 1

$\displaystyle\bf (17+a)(17-a)-(0,6-a)(a+0,6)=(17^{2} -a^{2} )-(0,6^{2} -a^{2} )=\\\\ =289-a^{2} -0,36+a^{2} =289-0,36=288,64$

В ответе не содержится переменная , значит значение выражения от неё не зависит .

Answer 2

Mathematical Expression Analysis

To prove that the expression a(4 - a)(17 + a)(17 - a) - (0.6 - a)(a + 0.6) does not depend on the variable a, we can simplify the expression and show that it does not contain a.

First, let's expand the expression and simplify it.

Expanding the expression: a(4 - a)(17 + a)(17 - a) - (0.6 - a)(a + 0.6)

Simplifying the expression: 4a(17^2 - a^2) - (0.6 - a)(a + 0.6)

Now, let's further simplify the expression to see if it depends on the variable a.

Further Simplification

Expanding and simplifying the expression: 4a(289 - a^2) - (0.6a + 0.6a - a^2 - 0.36)

Simplifying further: 1156a - 4a^3 - 1.2a - 0.36 - a^2

Combining like terms: -4a^3 - a^2 + 1156a - 1.2a - 0.36

Finally, we have the simplified expression: -4a^3 - a^2 + 1154.8a - 0.36

Conclusion

After simplifying the given expression, it is evident that the resulting expression contains the variable a. Therefore, the value of the expression does depend on the variable a.

This concludes the analysis of the given mathematical expression.