Question

7qp/7q-p * (7q/p - p/7q) при q=√3 - 5 при p=42-7√3

Answer 1

7qp/7q-p * (49q^2-p^2)/7pq= (7q-p)*(7q+p)/7p-q= 7q+p= 7(\|3-5)+42-7\|3= 7\|3-35+42-7\|3= 7

Answer 2

To solve the expression, let's substitute the given values of q and p into the expression and perform the calculations step by step:

Given values: q = √3 - 5 p = 42 - 7√3

Expression: (7q/p) - (p/7q)

Step 1: Substitute the values of q and p into the expression:

(7(√3 - 5)/(42 - 7√3)) - ((42 - 7√3)/(7(√3 - 5)))

Step 2: Simplify the expression:

To simplify the expression, we'll first rationalize the denominators:

For the first term, we multiply both the numerator and denominator by the conjugate of the denominator, which is (42 + 7√3):

(7(√3 - 5)/(42 - 7√3)) * ((42 + 7√3)/(42 + 7√3))

For the second term, we do the same:

((42 - 7√3)/(7(√3 - 5))) * ((42 + 7√3)/(42 + 7√3))

Step 3: Perform the multiplications in both terms:

First term: (7(√3 - 5)(42 + 7√3)) / ((42 - 7√3)(42 + 7√3))

Second term: ((42 - 7√3)(42 + 7√3)) / (7(√3 - 5)(42 + 7√3))

Step 4: Continue simplifying:

First term: (7√3 * 42 + 7√3 * 7√3 - 35 * 42 - 35 * 7√3) / (42^2 - (7√3)^2)

Second term: (42^2 - (7√3)^2) / (7√3 * 42 + 7√3 * 7√3 - 35 * 42 - 35 * 7√3)

Step 5: More simplification:

First term: (294√3 + 147 - 1470 - 245√3) / (1764 - 147)

Second term: (1764 - 147) / (294√3 + 147 - 1470 - 245√3)

Step 6: Final simplification:

First term: (-951√3 - 1323) / 1617

Second term: (1617) / (-951√3 - 1323)

Step 7: Subtract the second term from the first:

((-951√3 - 1323) / 1617) - (1617 / (-951√3 - 1323))

Step 8: To subtract the fractions, find a common denominator:

The common denominator is (1617) * (-951√3 - 1323):

[(1617 * (-951√3 - 1323)) / (1617 * (-951√3 - 1323))] * ((-951√3 - 1323) / 1617) - [(1617 * 1617) / (1617 * (-951√3 - 1323))] * (1617 / (-951√3 - 1323))

Step 9: Perform the subtraction:

(-1617^2 + 1617^2) / (1617 * (-951√3 - 1323))

Step 10: The expression simplifies to:

0 / (1617 * (-951√3 - 1323)) = 0

Therefore, the value of the expression is 0.