Question

108. Докажите неравенство: a) (5-2/3)(6+5/3) > 13; б) (3 – 1)/2 + 1) > (2 + 2)(3 – 2). пожалуйста помогите ​

Answer 1

а)

$(5- \frac{2}{3} ) \times (6 + \frac{5}{3}) = 4\frac{1}{2} + 6 \frac{5}{3} = 4 \frac{3}{6} + 6 \frac{10}{6} = 10 \frac{13}{6} = 12 \frac{1}{6}$

под буквой б) не понятно

Answer 2

Proof of Inequality:

a) To prove the inequality (5 - 2/3)(6 + 5/3) > 13, let's simplify the expression step by step:

Step 1: Simplify the terms inside the parentheses: - (5 - 2/3) = (15/3 - 2/3) = 13/3 - (6 + 5/3) = (18/3 + 5/3) = 23/3

Step 2: Multiply the simplified terms: - (13/3)(23/3) = 299/9

Step 3: Compare the result to 13: - 299/9 > 13

Therefore, the inequality (5 - 2/3)(6 + 5/3) > 13 is true.

b) To prove the inequality (3 + -1)/2 + 1 > (2 + 2)(3 + -2), let's simplify the expression step by step:

Step 1: Simplify the terms inside the parentheses: - (3 + -1)/2 = 2/2 = 1 - (2 + 2)(3 + -2) = 4 * 1 = 4

Step 2: Add 1 to both sides of the inequality: - 1 + 1 > 4 + 1 - 2 > 5

Therefore, the inequality (3 + -1)/2 + 1 > (2 + 2)(3 + -2) is false.