Question

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Answer 1

Explicație pas cu pas:

a)

$A(x) = {x}^{2} + 3x - 10 = {x}^{2} + 5x - 2x - 10 = \\ = x(x + 5) - 2(x + 5) = \bf (x + 5)(x - 2)$

$B(x) = {x}^{2} - 6x = \bf x(x - 6)$

b)

$A( \sqrt{5} - 1) = {(\sqrt{5} - 1)}^{2} + 3(\sqrt{5} - 1) - 10 = \\ = 5 - 2 \sqrt{5} + 1 + 3 \sqrt{5} - 3 - 10 = \bf \sqrt{5} - 7$

c)

$A (x) = {(x - 4)}^{2}$

${x}^{2} + 3x - 10 = {x}^{2} - 8x + 16$

$3x + 8x = 16 + 10$

$11x = 26 \implies x = \bf \frac{26}{11}$

d)

$10 + B(a) = 10 + {a}^{2} - 6a = {a}^{2} - 6a + 9 + 1 = {(a - 3)}^{2} + 1$

$\red{ \bf {(a - 3)}^{2} + 1 > 0}$

=>

$10 + B(a) \not = 0$

∀a ∈ R