Question

procedimiento (╥﹏╥)(╥﹏╥)​

Answer 1

Explicación paso a paso:

19. Simplificar:

$S=\sqrt{[(x+2)(x+5)]^{2} -(x+1)(x+2)(x+5)(x+6)+9}$

Resolvamos:

$S=\sqrt{[(x+2)(x+5)]^{2} -(x+1)(x+2)(x+5)(x+6)+9} \\\\S=\sqrt{(x+2)(x+5)[(x+2)(x+5) -(x+1)(x+6)]+9} \\\\S=\sqrt{(x+2)(x+5)[(x^{2} +7x+10) -(x^{2} +7x+6)]+9} \\\\S=\sqrt{(x+2)(x+5)[x^{2} +7x+10 -x^{2} -7x-6]+9} \\\\S=\sqrt{(x+2)(x+5)[4]+9}\\\\S=\sqrt{4(x+2)(x+5)+9} \\\\S=\sqrt{4x^{2} +28x+40+9} \\\\S=\sqrt{4x^{2} +28x+49} \\\\S=\sqrt{(2x+7)^{2} } \\\\S=2x+7$

Por lo tanto, el valor de S es 2x+7

20. De: x(x - 3) = -1

Calcular R = x⁹ + x⁻⁹

De x(x - 3) = -1, entonces:

x(x - 3) = -1

x - 3 = -1/x

x + 1/x = 3

x + x⁻¹ = 3

Resolvamos:

x + x⁻¹ = 3

(x + x⁻¹)³ = (3)³

(x)³ + 3(x)²(x⁻¹) + 3(x)(x⁻¹)² + (x⁻¹)³ = 27

x³ + 3(x²)(x⁻¹) + 3(x)(x⁻²) + x⁻³ = 27

x³ + 3x + 3x⁻¹ + x⁻³ = 27

x³ + 3(x + x⁻¹) + x⁻³ = 27

x³ + 3(3) + x⁻³ = 27

x³ + x⁻³ +9 = 27

x³ + x⁻³ = 27-9

x³ + x⁻³ =  18

Hallamos E:

x³ + x⁻³ = 18

(x³ + x⁻³)³ = (18)³

(x³)³ + 3(x³)²(x⁻³) + 3(x³)(x⁻³)² + (x⁻³)³ = 5832

x⁹ + 3(x⁶)(x⁻³) + 3(x³)(x⁻⁶) + x⁻⁹ = 5832

x⁹ + 3x³ + 3x⁻³ + x⁻⁹ = 5832

x⁹ + 3(x³ + x⁻³) + x⁻⁹ = 5832

x⁹ + 3(18) + x⁻⁹ = 5832

x⁹ + x⁻⁹ +54 = 5832

x⁹ + x⁻⁹ = 5832-54

x⁹ + x⁻⁹ = 5778

R =  5778

Por lo tanto, el valor de R es 5778