Question

A^2/a^2-7ab:a/a^2-49b^2 при a=6+7кореня из 2,b=4- корень из 2

Answer 1

Ответ:

34+6$\sqrt{2}$

Объяснение:

$\frac{a^2}{a^2-7ab} : \frac{a}{a^2-49b^2}$ =  $\frac{a^2}{a*(a-7b)} *\frac{a^2-49b^2}{a}$ =

$\frac{a}{a*(a-7b)} * (a-7b)*(a+7b)$ =  $\frac{a}{a} * (a+7b)$ = $a + 7b$

==>

6+7$\sqrt{2}$ + 7*4 - $\sqrt{2}$ = 34 + 7$\sqrt{2}$ - $\sqrt{2}$ = 34 + 6$\sqrt{2}$

Answer 2

To simplify the expression A^2/(a^2 - 7ab) : a/(a^2 - 49b^2) with the given values of a and b, we first need to find the value of A.

Given: a = 6 + 7√2 b = 4 - √2

To find A, we can use the fact that A = a - b:

A = (6 + 7√2) - (4 - √2) A = 6 + 7√2 - 4 + √2 A = 2 + 8√2

Now we can substitute the values of A, a, and b into the expression:

Expression = A^2/(a^2 - 7ab) : a/(a^2 - 49b^2)

Expression = (2 + 8√2)^2 / ((6 + 7√2)^2 - 7(6 + 7√2)(4 - √2)) : (6 + 7√2) / ((6 + 7√2)^2 - 49(4 - √2)^2)

Expression = (4 + 32√2 + 128)/(36 + 84√2 + 492 - 28√2 - 7√2) : (6 + 7√2)/(36 + 84√2 + 492 - 49*2)

Expression = (132 + 32√2)/(85√2 + 36) : (6 + 7√2)/(85√2 - 13)

To rationalize the denominators, we need to multiply both the numerator and denominator of each fraction by the conjugate of the denominator:

Expression = ((132 + 32√2)/(85√2 + 36)) * ((85√2 - 13)/(85√2 - 13)) : ((6 + 7√2)/(85√2 - 13)) * ((85√2 + 36)/(85√2 + 36))

Now, let's simplify the fractions:

Numerator: (132 + 32√2)(85√2 - 13) = 11220√2 - 1716 + 2720√2 - 416√2 = 13804√2 + 1304

Denominator: (85√2 + 36)(85√2 - 13) = 7225*2 - 1105√2 + 3060√2 - 468 = 14450 - 740√2

Expression = (13804√2 + 1304)/(14450 - 740√2) : (6 + 7√2)/(85√2 - 13)

To divide fractions, multiply by the reciprocal of the second fraction:

Expression = (13804√2 + 1304)/(14450 - 740√2) * (85√2 - 13)/(6 + 7√2)

Now, let's simplify further:

Numerator: (13804√2 + 1304)(85√2 - 13) = 1174340 - 178412√2 + 109520√2 - 16852√2 = 1174340 - 68932√2

Denominator: (14450 - 740√2)(6 + 7√2) = 86700 - 12640√2 + 10150√2 - 1480 = 85220 - 11490√2

Expression = (1174340 - 68932√2)/(85220 - 11490√2)

That's the simplified form of the expression with the given values of a and b.