Question

NEED HELP PLEASE- ANSWER BOTH TASKS, WILL MARK BRAINLIEST

Task 1 - Nonlinear Systems of Equations

Create a system of equations that includes one linear equation and one quadratic equation.
-
Part 1. Show all work in solving your system of equations algebraically.
-
Part 2. Graph your system of equations and show the solution graphically to verify your solution.
-
Task 2 - Polynomial Identities

Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
-
Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a3 + b3 = (a + b)(a2 − ab + b2) to calculate the sum of the cubes of your numbers without using a calculator.
-

Answer 1

Answer:

f(x)5.79(3)^2 for task 1

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Task 1:

Non linear systems of equations:

x + y = 1 -------------------(I)     {Linear equation}

     y =  1 - x

y = x² - 5 ---------------(II)   {Quadratic equation}

Substitute y =1 - x in equation (II)

(II) -->   1 -x = x² -5

Add 'x' to both sides

1 = x² + x - 5

0 = x² + x - 5 - 1   {Subtract 1 from both sides}

x² + x - 6 = 0

x² + 3x - 2x - 6 = 0    {Rewrite the middle term}

x( x + 3) - 2(x + 3) = 0    

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

x + 3 = 0       ;  x - 2 = 0

x = - 3   ; x = 2

When x =  - 3 ,   y = 1 -(-3 )

                              = 1 + 3

                             y = 4

When x = 2  ; y = 1 - 2 = -1

Solution of the equations:  (-3,4)  & ( 2,-1)

Task 2:

Part 1: x = 40   ; y = 30

(x - y)² = x² - 2xy + y²

(40 - 30)² = 40² - 2*40*30 + 30²

               = 1600 - 2400 + 900

               = 2500 - 2400

                = 100

Part 2:

a = 10 , b = 11

a³ + b³ = (a + b)(a² - ab +b²)

(10)³ + (11)³ = (10 +11)(10² -10*11 + 11² )

              = 21* (100 - 110 + 121)

              = 21 * ( 221 - 110)

              = 21 * 111

              = 2331