How To Solve Problems Creatively?

How do you solve these algebra problems?

• please help me!! i don't understand this at all... It would be greatly appreciated if you did it step by step so I can try to learn how to do it. thank-you so much =) Simplify each expression: 13) (7 - 4i)(10 - 2i) Solve each Quadratic equation: 32) 2x^2 + 6x + 12 = 0 Write a polynomial function with rational coefficients in standard form with the given zeros: 10) x = 1, 2, (3/5) Solve each equation: 20) x^3 - 2x^2 + x = 0 Simplify each expression. Rationalize all denominators. Assume that all variables are positive. 7) √(7x^4y) / √(63xy^2) Solve each equation. Assume that all variables are positive: 20) (3x + 4)^(1/3) = -5 Solve each equation: 34) x^(x - 1) = 24 Use the properties of logarithms to simplify each equation and solve it. Round to thousandths: 42) ln (2x - 1)^2 = 7

• Answer:

  13) To simplify the expression (7 - 4i)(10 - 2i) all you have to do is multiply the binomials together. 7*(10-2i)=70-14i -4i*(10-2i)= -40i+8i^2 i^2 always is equal to -1 so replace the i^2 with a -1. this will make the second part -40i-8 Then combine like terms. -8+70= 62 -14i-40i=-54i So your final answer would be 62-54i 32) to solve 2x^2+6x+12 you must use the quadratic formula since it is not solvable by factoring. a=2 b=6 c=12 Plug these numbers into the quadratic formula. x = [-b+/-√(b^2-4ac)]/2a x = [-6+/-√(6^2-4*2*12)]/2*2 x = [-6+/-√(36-96)]/4 x = [-6+/-√(-60)]/4 From here factor out √(-60) the factors of -60 are 6 and 10 the factors of 6 are 2 and 3 and the factors of 10 are 2 and 5 you have a pair of 2s so pull them out along with an i since it is negative. Multiply 3*5 because that is what you have left over and you get: 2i*√(15) Plug this back into your equation giving you x = [-6+/- 2i√(15)]/4 When you simplify you get the final answer of [-3 +/- i √(15)]/2 10) to write this equation you have to work backwards. They give you the zeroes of 1,2, and (3/5) Set these equal to x and then move them to the side with the x. x=1 gives you x-1=0 x=2 gives you x-2=0 With 3/5 you have to multiply x by 5 then add 3 to get the polynomial. x= 3/5 5x=3 5x-3=0 So now you have the 3 polynomials (x-1)(x-2) and (5x-3) multiply them together to get the original equation. First multiply (x-1)*(x-2) x*(x-2)= x^2-2x -1*(x-2)= -x+2 -2x-x=-3x x^2-3x+2 is what you get then you multiply this with (5x-3). (5x-3)*(x^2-3x+2) 5x*(x^2-3x+2)=5x^3-15x^2+10x -3*(x^2-3x+2)=-3x^2+9x-6 Combine like terms and you get 5x^3-18x^2+19x-6 7) To simplify √(7x^4y) / √(63xy^2) all you have to do is multiply both top and bottom by √(63xy^2) When you do it to the bottom it gets rid of the square root leaving you with 63xy^2. To get the top just multiply them together. √(7x^4y)*√(63xy^2) would just give you √(7x^4y*63xy^2) So your final answer you just be √(7x^4y*63xy^2) / 63xy^2 20) To solve (3x + 4)^(1/3) = -5 you must first get rid of the 1/3 power. you do this y multiplying the powers of both sides by 3. -5 has and understood power of 1 so 1*3=3 and (1/3)*3=1 This gives you 3x+4=-5^3 Now do the power then get x alone. 3x+4=-125 Subtract 4 3x=-129 Divide by 3 Your final answer is x=-43 34) I am unsure how to solve x^(x - 1) = 24 but through the magic of guess and check I got the answer x=3.524 42) To solve ln (2x-1)^2 = 7 you first must get rid of the ln on the left side. to do this you "base" both sides. The base of ln is the number e. When you base both sides you end up with (2x-1)^2=e^7 Do the exponents to simplify (2x-1)^2= 1096.628 Square root both sides. 2x-1= 33.115 add one 2x=34.115 divide by two x=17.058 your final answer I hope this helped. Sorry for not being able to solve 34.