Mathematics: Solve the equation for x. √x-6+3=10

Solve the equation for x. √x-6+3=10 - id631013541935, myleefaustin

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cabreradesirae4807

12.02.2022

Mathematics

(a) 5x^2+7x-4

(b) $\text{Length of the third side=}5x^3 -x^2-8x+1$

(c)Yes

Step-by-step explanation:

Side 1: 3x^2-2x-1

Side 2: 9x + 2x^2-3

Perimeter= 5x^3 + 4x^2-x-3

(a)Total length of the two sides, 1 and 2, of the triangle

$(3x^2-2x-1)+(9x + 2x^2-3)\\=3x^2-2x-1+9x + 2x^2-3\\$Colect like terms\\=3x^2+ 2x^2-2x+9x-1-3\\=5x^2+7x-4$

(b)Length of the third side of the triangle

Since the perimeter is given, and we have the sum of the other two sides, we simply subtract it from the perimeter,

$(5x^3 + 4x^2-x-3)-(5x^2+7x-4)\\=5x^3 + 4x^2-x-3-5x^2-7x+4\\=5x^3 + 4x^2-5x^2-x-7x-3+4\\$Length of the third side=5x^3 -x^2-8x+1$

(c)When adding or subtracting polynomials, their variables and exponents do not change. Only the coefficients will change as in Part (a) and (b). Therefore, polynomials are closed under addition and subtraction.

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Solve the equation for x. √x-6+3=10

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