Let’s arrange the fist equation
x+y=12
2x+3y=29

Multiply equation 1 by 2
So it will be

2x+2y=24

Subtract eq 1 from eq 2

2x+3y=29
2x+2y=24
—————-
Y =5

Put value of y in eq 1

2x+2y=24
2x +10= 24
2x= 24-10
2x= 14
x=14/2
x=7

S.S= (7,5)

8 0

3 years ago

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What is the completely factored form of d4 -8d2 + 16

irinina [24]

According to Vieta's Formulas, if $x_1,x_2$ are solutions of a given quadratic equation:

$ax^2+bx+c=0$

Then:

$a(x-x_1)(x-x_2)$ is the completely factored form of $ax^2+bx+c$ .

If choose $x=d^2$ , then:

$\displaystyle x^2-8x+16=0\\\\x_{1,2}= \frac{8\pm \sqrt{64-64} }{2}=4$

So, according to Vieta's formula, we can get:

$x^2-8x+16=(x-4)(x-4)= (x-4)^2$

But $x=d^2$ :

$d^4-8d^2+16=(d^2-4)^2=[(d+2)(d-2)]^2=(d+2)^2(d-2)^2$

8 0

3 years ago