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МатематикаВопрос:
700. Найдите значение выражения:
Ответ:
a) $$8x^2(x - 4) - (2x - 3)(4x^2 + 6x + 9) - 17$$ при $$x = 0.5$$.
$$8(0.5)^2(0.5 - 4) - (2(0.5) - 3)(4(0.5)^2 + 6(0.5) + 9) - 17 = 8(0.25)(-3.5) - (1 - 3)(4(0.25) + 3 + 9) - 17 = 2(-3.5) - (-2)(1 + 3 + 9) - 17 = -7 - (-2)(13) - 17 = -7 + 26 - 17 = 2$$.
б) $$4a^2(3a - 2) - 3a(2a - 1)^2 - (2a - 5)(2a + 5)$$ при $$a = 3.3$$.
$$4(3.3)^2(3(3.3) - 2) - 3(3.3)(2(3.3) - 1)^2 - ((2(3.3))^2 - 5^2) = 4(10.89)(9.9 - 2) - 9.9(6.6 - 1)^2 - (6.6^2 - 25) = 43.56(7.9) - 9.9(5.6)^2 - (43.56 - 25) = 344.124 - 9.9(31.36) - 18.56 = 344.124 - 310.464 - 18.56 = 15.1$$.
в) $$(9x^2 - 3xb + b^2)(3x + b) - 9x(3x^2 - b) - b^3$$ при $$x = -1/3$$, $$b = 2/3$$.
$$(9x^2 - 3xb + b^2)(3x + b) = (3x)^3 + b^3 = 27x^3 + b^3$$.
$$27x^3 + b^3 - 27x^3 + 9xb - b^3 = 9xb$$.
При $$x = -1/3$$, $$b = 2/3$$: $$9(-1/3)(2/3) = -6/3 = -2$$.
г) $$x(3x - 2y)(3x + 2y) - x(3x + 2y)^2 + 2xy(5x + 2y)$$ при $$x = 0.5$$, $$y = -1$$.
$$x(9x^2 - 4y^2) - x(9x^2 + 12xy + 4y^2) + 10x^2y + 4xy^2 = 9x^3 - 4xy^2 - 9x^3 - 12x^2y - 4xy^2 + 10x^2y + 4xy^2 = -2xy^2 - 2x^2y$$.
При $$x = 0.5$$, $$y = -1$$: $$-2(0.5)(-1)^2 - 2(0.5)^2(-1) = -2(0.5)(1) - 2(0.25)(-1) = -1 + 0.5 = -0.5$$.
$$8(0.5)^2(0.5 - 4) - (2(0.5) - 3)(4(0.5)^2 + 6(0.5) + 9) - 17 = 8(0.25)(-3.5) - (1 - 3)(4(0.25) + 3 + 9) - 17 = 2(-3.5) - (-2)(1 + 3 + 9) - 17 = -7 - (-2)(13) - 17 = -7 + 26 - 17 = 2$$.
б) $$4a^2(3a - 2) - 3a(2a - 1)^2 - (2a - 5)(2a + 5)$$ при $$a = 3.3$$.
$$4(3.3)^2(3(3.3) - 2) - 3(3.3)(2(3.3) - 1)^2 - ((2(3.3))^2 - 5^2) = 4(10.89)(9.9 - 2) - 9.9(6.6 - 1)^2 - (6.6^2 - 25) = 43.56(7.9) - 9.9(5.6)^2 - (43.56 - 25) = 344.124 - 9.9(31.36) - 18.56 = 344.124 - 310.464 - 18.56 = 15.1$$.
в) $$(9x^2 - 3xb + b^2)(3x + b) - 9x(3x^2 - b) - b^3$$ при $$x = -1/3$$, $$b = 2/3$$.
$$(9x^2 - 3xb + b^2)(3x + b) = (3x)^3 + b^3 = 27x^3 + b^3$$.
$$27x^3 + b^3 - 27x^3 + 9xb - b^3 = 9xb$$.
При $$x = -1/3$$, $$b = 2/3$$: $$9(-1/3)(2/3) = -6/3 = -2$$.
г) $$x(3x - 2y)(3x + 2y) - x(3x + 2y)^2 + 2xy(5x + 2y)$$ при $$x = 0.5$$, $$y = -1$$.
$$x(9x^2 - 4y^2) - x(9x^2 + 12xy + 4y^2) + 10x^2y + 4xy^2 = 9x^3 - 4xy^2 - 9x^3 - 12x^2y - 4xy^2 + 10x^2y + 4xy^2 = -2xy^2 - 2x^2y$$.
При $$x = 0.5$$, $$y = -1$$: $$-2(0.5)(-1)^2 - 2(0.5)^2(-1) = -2(0.5)(1) - 2(0.25)(-1) = -1 + 0.5 = -0.5$$.
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