4. If 6' + 7 !-8t, find x
The given equation is 1 6 ! + 1 7 ! = x 8 ! .
The formula to calculate n ! is defined as,
n ! = 1 × 2 × 3 × ⋯ × ( n − 1 ) × n
To take the common factor from denominator, factorize the bigger term in factorials.
The formula to calculate the factors of a factorial in terms of factorial itself is,
n ! = n ( n − 1 ) ! n ! = n ( n − 1 ) ( n − 2 ) ! [ n ≥ 2 ] ⋮
The given equation can be written as,
1 6 ! + 1 7 × 6 ! = x 8 × 7 × 6 !
Take 1 6 ! common from left hand side and cancel with 1 6 ! from right side of the equation.
1 6 ! ( 1 + 1 7 ) = x 8 × 7 × 6 ! 1 + 1 7 = x 8 × 7 8 7 = x 8 × 7
Cross multiply the above equation, to find the value of x.
x = 8 × 8 × 7 7 = 64
Thus, the value of x is 64.
The given equation is
The formula to calculate
To take the common factor from denominator, factorize the bigger term in factorials.
The formula to calculate the factors of a factorial in terms of factorial itself is,
The given equation can be written as,
Take
Cross multiply the above equation, to find the value of x.
Thus, the value of x is 64.
