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Hi,

1. a³-9a²+14a=0

a(a² - 9a + 14) = 0

a(a - 7)(a - 2) = 0

a = 0 or 7 or 2 <==ANSWER

2. x^4 -14x²+45=0

(x² - 9)(x² - 5) = 0

(x - 3)(x + 3)(x² - 5) = 0

x² - 5 = 0

x² = 5 or x - 3 = 0 or x + 3 = 0

x = ±√5 or x = 3 or x = -3 <==ANSWER

3. x^4-13x²+36=0

(x² - 9)(x² - 4) = 0

(x - 3)(x + 3)(x - 2)(x + 2) = 0

x = 3 or -3 or 2 or -2 <==ANSWER

4. x³ = 3x²

x³ - 3x² = 0

x²(x - 3) = 0

x² = 0 or x - 3 = 0

x = 0 or x = 3 <==ANSWER

(0 is a double root)

I hope that helps!! :-)

Algebraic Mathematics.

(1) a^3-9a^2+14a=0,

14a+a^2(a-9)=0,

a(14+a(a-9))=0,

a=0

(2) x^4-13x^2=0,

(x^2-13)x^2+36=0,

x=3

(3) x^3=3x^2,

x^3-3x^2=0,

x^2(x-3)=0,

x=0 or x=3

1. a³-9a²+14a=0

a(a-7)(a-2)=0

Answers are a=0,2 and 7.

2. f(x)=x^4 -14x²+45

if x=3,then x^4 -14x²+45=0,so (x-3) is a factor of f(x)

(x-3)(ax^3+bx^2+cx+d)=x^4 -14x²+45

You get a=1,b=3,c= -5 and d= -15

But I leave it to you to find the other value/s of x.I give you one hint:

set g(x)=x^3+3x^2-5x-15 and find a value of x that makes g(x)=0 and follow the same method I showed you earlier

3. f(x)=x^4-13x²+36

if x=2,then f(x)=0,so (x-2) is a factor of f(x)

(x-3)(ax^3+bx^2+cx+d)=x^4-13x²+36

You get a=1,b=2,c= -9 and d= -18

Now g(x)=x^3+2x^2-9x-18

if x= -2,g(x)=0,so (x+2) is a factor of g(x)

(x+2)(kx^2+lx+m)=x^3+2x^2-9x-18

You get k=1,l=0 and m= -9,so the other factors of g(x) are (x+3) and (x-3).You can now infer what the values of x need to be.

4. x³-3x²=0

(x^2)(x-3)=0

You can now infer what the values of x need to be.

one million) 9r-2-6r=11 9r - 6r = 11 + 2 3r = 13 r = 13/3 answer 2) n - 3(one million + 2n)= 17 n - 3 - 6n = 17 n - 6n = 17 + 3 - 5n = 20 n = 20/-5 n = - 4 answer 3) 12x + ninety six = 12 12x = 12 - ninety six 12x = - eighty 4 x = - eighty 4/12 x = - 7 answer 4) 24 - 3x = 9x 24 - 3x - 9x = 0 - 3x - 9x = - 24 - 12x = - 24 x = - 24/-12 x = 2 answer 5) 15x - 23 = 15x 15x - 15x - 23 = 0 0 = 23 (No answer) answer 6) 12 + 11h = -18 - 4h 12 + 11h + 4h = - 18 11h + 4h = - 18 - 12 15h = - 30 h = - 30/15 h = - 2 answer 7) 5x - 9 = 18x - 23 5x - 18x - 9 = - 23 5x - 18x = - 23 + 9 - 13x = - 14 x = - 14/-13 x = 14/13 answer 8) 13.7t - 4.7 = 9.9 + 8.1t 13.7t - 8.1t = 9.9 + 4.7 5.6t = 14.6 t = 14.6/5.6 or 2.607 answer wish this facilitates you. teddy boy

a² - 9/2a = - 14 + (- 9/2)²

a² - 9/2a = (- 56 + 81)/4

(a - 9/2)² = 25/4

a - 9/2 = ± 5/2

a = (9 + 5)/2, a = 14/2, a = 7

a = (9 - 5)/2, a = 4/2, a = 2

Answer 1: a = 0, 7, 2; factors: a(a - 7)(a - 2)

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Let u = x²:

u² - 14u = - 45

u² - 7u = - 45 + (- 7)²

u² - 7u = - 45 + 49

(u - 7)² = 4

u - 7 = ± 2

u = 7 + 2, u = 9

u = 7 - 2, u = 5

x² = 9, x = ± 3

x² = 5, x = ± √5

Answer 2: x = 3, - 3, ± √5

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u² - 13/2u = - 36 + (- 13/2)²

u² - 13/2u = (- 144 + 169)/4

(u - 13/2)² = 25/4

u - 13/2 = ± 5/2

u = (13 + 5)/2, u = 18/2, u = 9

u = (13 - 5)/2, u = 8/2, u = 4

x² = 9, x = ± 3

x = 4, x = ± 2

Answer 3: x = 3, - 3, 2, - 2

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x³ = 3x²

x = 3

Answer 4: x = 0, 3

1) a ( a^2 - 9a + 14) = 0

a ( a- 7) ( a-2) = 0

a = 0, 7 , 2 ANSWER

2) ( x^2 -9) ( x^2 -5) = 0

( x+3) ( x-3) ( x+ \/5) ( x-\/5) = 0

x = -3 , 3, - \/5 , \/5 ANSWER

3) ( x^2 - 9) ( x^2 -4) = 0

( x+3) ( x-3) ( x-2) ( x+2) = 0

x = -3, 3, 2, -2 ANSWER

4) x^3 = 3x^2

x = 3 Or 0 ANSWER

1. a³-9a²+14a=0

a(a²-9a+14)=0

a(a-7)(a-2)=0

a=0, 2 or 7

2. Let y=x²

y²-14y+45=0

(y-9)(y-5)=0

y=9 or 5

x²=9 or 5

x=-3, -rt(5), rt(5) or 3

3. Let y=x²

Therefore:

y²-13y+36=0

(y-4)(y-9)=0

y=4 or 9

x²=4 or 9

x=-3,-2,2 or 3

4. x³=3x²

x³-3x²=0

x²(x-3)=0

x=0 or 3