+0

# system

0
18
1
+1475

One ordered pair \$(a,b)\$ satisfies the two equations  \$ab^4 = 48\$ and \$a^2 = 24\$.  What is the value of \$b\$ in this ordered pair?

Jan 1, 2024

#1
+1024
+2

One ordered pair \$(a,b)\$ satisfies the two equations  \$ab^4 = 48\$ and \$a^2 = 24\$.  What is the value of \$b\$ in this ordered pair?

a2  =  24    ===>    a  =  sqrt(24)

ab4  =  48

sqrt(24) • b4  =  48

48

b4  =  ––––––––

sqrt(24)

Multiply right hand side by

sqrt(24) / sqrt(24) which is

simply multiplying it by one.                                                   48              sqrt(24)

b4  =  ––––––––  •   ––––––––

sqrt(24)         sqrt(24)

48 •  sqrt(24)

b4  =   ––––––––––––

24

b4  =  2 • sqrt(24)

b4  =  sqrt(96)

b4  =  961/2

b  =  (961/2)1/4

b  =  961/8

From root function on scientific calculator                  b  =  1.769228

.

Jan 1, 2024

#1
+1024
+2

One ordered pair \$(a,b)\$ satisfies the two equations  \$ab^4 = 48\$ and \$a^2 = 24\$.  What is the value of \$b\$ in this ordered pair?

a2  =  24    ===>    a  =  sqrt(24)

ab4  =  48

sqrt(24) • b4  =  48

48

b4  =  ––––––––

sqrt(24)

Multiply right hand side by

sqrt(24) / sqrt(24) which is

simply multiplying it by one.                                                   48              sqrt(24)

b4  =  ––––––––  •   ––––––––

sqrt(24)         sqrt(24)

48 •  sqrt(24)

b4  =   ––––––––––––

24

b4  =  2 • sqrt(24)

b4  =  sqrt(96)

b4  =  961/2

b  =  (961/2)1/4

b  =  961/8

From root function on scientific calculator                  b  =  1.769228

.

Bosco Jan 1, 2024