Question

7ab/a+4b*(a/4b-4b/a) при а=4 √(3) + 8 и при в=√(3) - 5

Answer 1

Ответ:

См фото

Объяснение:

Answer 2

To evaluate the expression 7ab/a+4b*(a/4b-4b/a) with a = 4√3 + 8 and b = √3 - 5, we can substitute the given values into the expression and simplify step by step. Let's calculate it:

Step 1: Substitute the values of a and b into the expression: 7(4√3 + 8)(√3 - 5)/(4√3 + 8) + 4(√3 - 5)*((4√3 + 8)/(4(√3 - 5)) - (4(√3 - 5))/(4√3 + 8))

Step 2: Simplify the expression: = 7(4√3 + 8)(√3 - 5)/(4√3 + 8) + 4(√3 - 5)((4√3 + 8)/(4(√3 - 5)) - (4(√3 - 5))/(4√3 + 8)) = 7(4√3 + 8)(√3 - 5)/(4√3 + 8) + 4(√3 - 5)((4√3 + 8)/(4√3 - 20) - (4√3 - 20)/(4√3 + 8))

Step 3: Simplify further: = 7(4√3√ - 20√3 + 8√3 - 40)/(4√3 + 8) + 4(√3(4√3 + 8))/(4√3 - 20) - 4(4√3 - 20)/(4√3 + 8)) = (28√3 - 140 + 56√3 - 40)/(4√3 + 8) + (16√3 + 32)/(4√3 - 20) - (16√3 - 80)/(4√3 + 8))

Step 4: Combine like terms and simplify the denominators: = (84√3 - 180)/(4√3 + 8) + (16√3 + 32)/(4√3 - 20) - (16√3 - 80)/(4√3 + 8))

Step 5: Find a common denominator and combine the fractions: = ((84√3 - 180)(4√3 - 20) + (16√3 + 32)(4√3 + 8) - (16√3 - 80)(4√3 + 8))/((4√3 + 8)(4√3 - 20))

Step 6: Expand and simplify: = (336√3 - 1680 - 180√3 + 900 + 64√3 + 128 - 64√3 - 320)/(16√3 - 80) = (200√3 + 708)/(16√3 - 80)

Therefore, the simplified expression is (200√3 + 708)/(16√3 - 80).