Question

if the number m is 3 less than number n and the sum of the squares of m and n is 29, find mn

Answer 1

Step-by-step explanation:

m - 3= n....(1)

m²+n²= 29...(2)

squaring both sides of eq (1)

m²- 9= n²

m²-n² =9...(3)

m²+n²= 29...(2)

- + -

Ans 2n² = -20

n² = -20/2

n²= -10

Answer 2

GIVEN

Let m and n be two unknown numbers where,

m = n - 3 ...eq.01

m^2 + n^2 = 29 ...eq.02

SOLUTION

Subtututing value of m from equation 01 in equation 02 we have,

(n - 3)^2 + n^2 = 29

=> n^2 + 3^2 - 6n + n^2 = 29

=> 2n^2 - 6n + 9 = 29

=> 2n^2 - 6n - 20 = 0

=> n^2 - 3n - 10 = 0

=> n^2 - 5n + 2n - 10 = 0

=> n(n - 5) + 2(n - 5) = 0

=> (n+2)(n - 5)

=> n = 5 or n = - 2

CASE - 01

n = 5, if n = 5

The other m = 5 - 3 = 2

Hence= m = 5 and n = 2

Case -02

If n = -2, then m = -2 -3 = -5

Hence the solutions are

n = -2 or 5 and m = -5 or 2

Now we have to find

mn = m × n = - 5 × -2 or 5 × 2

= 10 (Ans)

Therefore the value of mn is 10.