Question

А) (х + 4)2 = 3х + 40; б) (2x – 3)2 = 11х - 19; в) 3(х + 4)2 = 10x + 32; г) 15х2 +17 = 15(х + 1)2 = =

Answer 1

Ответ:А. -32; Б. 13/7; В -2; Г. 17/30

Объяснение:

Answer 2

Task:

The task provided consists of four equations, and we need to solve each equation for the variable x. Let's solve each equation step by step.

Equation a: (х + 4)2 = 3х + 40

To solve this equation, we can expand the square on the left side and then simplify the equation.

Expanding the square: (х + 4)2 = (х + 4)(х + 4) = х2 + 8х + 16

Now we can rewrite the equation: х2 + 8х + 16 = 3х + 40

Next, let's move all the terms to one side of the equation: х2 + 8х - 3х + 16 - 40 = 0

Simplifying: х2 + 5х - 24 = 0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use factoring in this case.

Factoring: (х + 8)(х - 3) = 0

Setting each factor equal to zero: х + 8 = 0 or х - 3 = 0

Solving for x: х = -8 or х = 3

Therefore, the solutions for equation a are x = -8 and x = 3.

Equation b: (2x – 3)2 = 11х - 19

Following the same steps as before, let's solve this equation.

Expanding the square: (2x - 3)2 = (2x - 3)(2x - 3) = 4x2 - 12x + 9

Rewriting the equation: 4x2 - 12x + 9 = 11x - 19

Moving all the terms to one side: 4x2 - 12x - 11x + 9 + 19 = 0

Simplifying: 4x2 - 23x + 28 = 0

This is another quadratic equation. Let's solve it using factoring.

Factoring: (4x - 7)(x - 4) = 0

Setting each factor equal to zero: 4x - 7 = 0 or x - 4 = 0

Solving for x: x = 7/4 or x = 4

Therefore, the solutions for equation b are x = 7/4 and x = 4.

Equation c: 3(х + 4)2 = 10x + 32

Let's solve this equation using the same steps.

Expanding the square: 3(х + 4)2 = 3(х + 4)(х + 4) = 3(х2 + 8х + 16) = 3х2 + 24х + 48

Rewriting the equation: 3х2 + 24х + 48 = 10x + 32

Moving all the terms to one side: 3х2 + 24х - 10x + 48 - 32 = 0

Simplifying: 3х2 + 14х + 16 = 0

This is another quadratic equation. Let's solve it using factoring.

Factoring: (3x + 4)(x + 4) = 0

Setting each factor equal to zero: 3x + 4 = 0 or x + 4 = 0

Solving for x: x = -4/3 or x = -4

Therefore, the solutions for equation c are x = -4/3 and x = -4.

Equation d: 15х2 + 17 = 15(х + 1)2

Let's solve this equation using the same steps.

Expanding the square: 15(х + 1)2 = 15(х + 1)(х + 1) = 15(х2 + 2х + 1) = 15х2 + 30х + 15

Rewriting the equation: 15х2 + 17 = 15х2 + 30х + 15

Moving all the terms to one side: 15х2 - 15х2 + 30х - 17 + 15 = 0

Simplifying: 30х - 2 = 0

Solving for x: 30х = 2 х = 2/30 х = 1/15

Therefore, the solution for equation d is x = 1/15.

In summary, the solutions for the given equations are: a) x = -8, x = 3 b) x = 7/4, x = 4 c) x = -4/3, x = -4 d) x = 1/15

Please let me know if you need any further assistance!