Question

якого найбільшого значення може набути вираз 100-(m+4)⁸ і за якого значення змінної

Answer 1

Ответ:

m = -4 -4√10

m = 4√10- 4

Объяснение:

Solve for m over the real numbers:

100 - (m + 4)^8 = 0

Subtract 100 from both sides:

-(m + 4)^8 = -100

Multiply both sides by -1:

(m + 4)^8 = 100

Take the square root of both sides:

(m + 4)^4 = 10 or (m + 4)^4 = -10

Take the square root of both sides:

(m + 4)^2 = sqrt(10) or (m + 4)^2 = -sqrt(10) or (m + 4)^4 = -10

Take the square root of both sides:

m + 4 = 10^(1/4) or m + 4 = -10^(1/4) or (m + 4)^2 = -sqrt(10) or (m + 4)^4 = -10

Subtract 4 from both sides:

m = 10^(1/4) - 4 or m + 4 = -10^(1/4) or (m + 4)^2 = -sqrt(10) or (m + 4)^4 = -10

Subtract 4 from both sides:

m = 10^(1/4) - 4 or m = -4 - 10^(1/4) or (m + 4)^2 = -sqrt(10) or (m + 4)^4 = -10

(m + 4)^2 = -sqrt(10) has no solution since for all m on the real line, (m + 4)^2>=0 and -sqrt(10)<0:

m = 10^(1/4) - 4 or m = -4 - 10^(1/4) or (m + 4)^4 = -10

(m + 4)^4 = -10 has no solution since for all m on the real line, (m + 4)^4 = ((m + 4)^2)^2>=0 and -10<0:

Answer: |

| m = 10^(1/4) - 4 or m = -4 - 10^(1/4)