Question

1)-0,7(-10)⁴-8•(-10)²-26=Решите хоть сколько 2)(√32-3)²3)x²+4x=21

Answer 1

1) -0.7 × (-10)^4 - 8 × (-10)^2 -26 = -0.7 × 10000 - 8 × 100 - 26 = -7000-800-26=-7826

2)(√32-3)² = 32 - 6√32 +9 = 41 -6√32

3) x^2 +4x -21=0

x1 = -7. x2 = 3

Answer 2

To solve the given equations, let's take them one by one:

1. $-0.7(-10)^4 - 8 \cdot (-10)^2 - 26$

Step 1: Perform the calculations within the parentheses first: $(-10)^4 = 10,000$ $(-10)^2 = 100$

Step 2: Continue evaluating the expression: $-0.7 \cdot 10,000 = -7,000$ $8 \cdot 100 = 800$

Step 3: Simplify the entire expression: $-7,000 - 800 - 26 = -7,826$

So, the value of the expression is $-7,826$.

2. $(\sqrt{32}-3)^2 \cdot 3x^2 + 4x = 21$

Step 1: Evaluate the expression within the parentheses: $\sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}$ $(\sqrt{32}-3)^2 = (4\sqrt{2} - 3)^2$

Step 2: Simplify the expression within the parentheses: $(4\sqrt{2} - 3)^2 = (4\sqrt{2} - 3)(4\sqrt{2} - 3) = 16 \cdot 2 - 12\sqrt{2} - 12\sqrt{2} + 9$ $(4\sqrt{2} - 3)^2 = 32 - 24\sqrt{2} + 9 = 41 - 24\sqrt{2}$

Step 3: Substitute this value back into the original equation: $(41 - 24\sqrt{2}) \cdot 3x^2 + 4x = 21$

Step 4: Rearrange the equation and set it to zero: $3x^2 \cdot (41 - 24\sqrt{2}) + 4x - 21 = 0$

Now, this is a quadratic equation in terms of $x$, and we can solve it using the quadratic formula.

Step 5: Quadratic Formula: The quadratic formula states that for an equation of the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In our equation, $a = 3(41 - 24\sqrt{2})$, $b = 4$, and $c = -21$.

Step 6: Calculate the discriminant ($\Delta$): $\Delta = b^2 - 4ac$

Step 7: Calculate the solutions for $x$: $x = \frac{-4 \pm \sqrt{\Delta}}{2 \cdot 3(41 - 24\sqrt{2})}$