ROUND 2 SPEED RACE
ONE EIGHTH STAGE 2026
Contest 19
Amaniampong SHS: 62
Ghanata SHS: 37
Tepa SHS: 31
Contest 20
Chemu SHTS: 52
Anglican SHS, Kumasi: 46
Mankranso SHS: 16
Contest 21
Bright SHS: 53
GSTS: 40
Presby SHTS, Aburi: 25
QUESTION
Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=7$.
ANSWER: 47
FORMULA
$M^2 + \frac{1}{M^2} = \left(M + \frac{1}{M}\right)^2 - 2$
SOLUTION
Take the given equation value:
$\left(M + \frac{1}{M}\right) = 7$
Square it directly:
$\left(M + \frac{1}{M}\right)^2 = 7^2 = 49$
Subtract 2 to obtain the final answer:
$M^2 + \frac{1}{M^2} = 49 - 2$
$M^2 + \frac{1}{M^2} = 47$
ANSWER: 47
PRACTICE QUESTIONS
1. Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=-9$.
ANSWER: $79$
SOLUTION
Square the given expression:
$\left(M+\dfrac{1}{M}\right)^2=M^2+2+\dfrac{1}{M^2}$
$(-9)^2=M^2+\dfrac{1}{M^2}+2$
$81=M^2+\dfrac{1}{M^2}+2$
$M^2+\dfrac{1}{M^2}=81-2=79$
2. Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=7$.
ANSWER: $47$
SOLUTION
Square the given expression:
$\left(M+\dfrac{1}{M}\right)^2=M^2+2+\dfrac{1}{M^2}$
$7^2=M^2+\dfrac{1}{M^2}+2$
$49=M^2+\dfrac{1}{M^2}+2$
$M^2+\dfrac{1}{M^2}=49-2=47$
3. Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=4$.
ANSWER: $14$
SOLUTION
Square the given expression:
$\left(M+\dfrac{1}{M}\right)^2=M^2+2+\dfrac{1}{M^2}$
$4^2=M^2+\dfrac{1}{M^2}+2$
$16=M^2+\dfrac{1}{M^2}+2$
$M^2+\dfrac{1}{M^2}=16-2=14$
4. Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=-3$.
ANSWER: $7$
SOLUTION
Square the given expression:
$\left(M+\dfrac{1}{M}\right)^2=M^2+2+\dfrac{1}{M^2}$
$(-3)^2=M^2+\dfrac{1}{M^2}+2$
$9=M^2+\dfrac{1}{M^2}+2$
$M^2+\dfrac{1}{M^2}=9-2=7$
5. Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=5$.
ANSWER: $23$
SOLUTION
Square the given expression:
$\left(M+\dfrac{1}{M}\right)^2=M^2+2+\dfrac{1}{M^2}$
$5^2=M^2+\dfrac{1}{M^2}+2$
$25=M^2+\dfrac{1}{M^2}+2$
$M^2+\dfrac{1}{M^2}=25-2=23$
6. Find the value of $M^2+\dfrac{1}{M^2}$, given $M+\dfrac{1}{M}=2$.
ANSWER: $2$
SOLUTION
Square the given expression:
$\left(M+\dfrac{1}{M}\right)^2=M^2+2+\dfrac{1}{M^2}$
$2^2=M^2+\dfrac{1}{M^2}+2$
$4=M^2+\dfrac{1}{M^2}+2$
$M^2+\dfrac{1}{M^2}=4-2=2$