Question

1) (3+х)^2-(х^2+3^2)-3^2=0 1 4 3 4 2) х(х +1 -- ) + -- - -- - ( -- + х^2 )=0 3 9 4 9

Answer 1

1)

$(3 + x) {}^{2} - (x {}^{2} + 3 {}^{2} ) - 3 {}^{2} = 0 \\ 9 + 6x + x {}^{2} - (x {}^{2} + 9) - 9 = 0 \\ 9 + 6x + x {}^{2} - x {}^{2} - 9 - 9 = 0 \\ 6x - 9 = 0 \\ 6x = 9 \\ x = \frac{ 9}{6} \\ x = \frac{3}{2}$

Answer 2

Let's solve each equation step by step:

1. (3 + х)^2 - (х^2 + 3^2) - 3^2 = 0

Step 1: Expand the squared terms: (3 + х)^2 = (3 + х)(3 + х) = 9 + 3х + 3х + х^2 = 9 + 6х + х^2 3^2 = 9

Step 2: Substitute the expanded terms into the original equation: (9 + 6х + х^2) - (х^2 + 9) - 9 = 0

Step 3: Simplify the equation: 9 + 6х + х^2 - х^2 - 9 - 9 = 0

Step 4: Combine like terms: 6х = 0

Step 5: Solve for х: Divide both sides by 6: х = 0

So the solution for the equation is х = 0.

2. х(х + 1/3) + 1/9 - 4/9 - (4/9 + х^2) = 0

Step 1: Distribute the terms in the first bracket: х^2 + (1/3)х + 1/9 - 4/9 - (4/9 + х^2) = 0

Step 2: Combine like terms: х^2 + (1/3)х + 1/9 - 4/9 - 4/9 - х^2 = 0

Step 3: Simplify the equation: (1/3)х - 7/9 = 0

Step 4: Move the constant term to the other side: (1/3)х = 7/9

Step 5: Solve for х: Multiply both sides by 3 to eliminate the fraction: х = (7/9) * 3

х = 7/3

So the solution for the equation is х = 7/3.