Question

(1/4х)-(4х+у/4ху) при х=√22, у=1/6

Answer 1

Решение смотри на фотографии

Answer 2

To evaluate the expression (1/4x) - ((4x + y)/(4xy)) when x = √22 and y = 1/6, we can substitute the given values into the expression and simplify it.

Let's calculate step by step:

1. Substitute x = √22 and y = 1/6 into the expression:

(1/4(√22)) - ((4(√22) + (1/6))/(4(√22)(1/6)))

2. Simplify the expression within the parentheses:

(1/4√22) - ((4√22 + 1/6)/(4√22/6))

3. Simplify further:

(1/4√22) - ((4√22 + 1/6)/(24√22))

4. Find a common denominator for the fractions:

(1/4√22) - ((24(4√22) + 24(1/6))/(24(24√22)))

5. Simplify the numerator of the second fraction:

(1/4√22) - ((96√22 + 4)/(576√22))

6. Combine the fractions with a common denominator:

(1 - (96√22 + 4)/(576√22))/(4√22)

7. Simplify the numerator:

(1 - 96√22 - 4)/(576√22))/(4√22)

8. Combine like terms:

(-95 - 96√22)/(576√22))/(4√22)

9. Simplify the denominator:

(-95 - 96√22)/(2304√22)

10. Multiply the numerator and denominator by the conjugate of the denominator to rationalize the denominator:

((-95 - 96√22)(2304√22))/(2304√22)(2304√22)

11. Simplify the numerator:

(-95(2304√22) - 96(2304√22)^2)/(2304√22)(2304√22)

12. Simplify further:

(-219,840√22 - 106,168,064)/(53,248√22)

Finally, the expression (1/4x) - ((4x + y)/(4xy)) when x = √22 and y = 1/6 is approximately:

(-219,840√22 - 106,168,064)/(53,248√22)