The number of...

Question

The number of ordered triples (a,b,c) of positive integers which satisfy the simultaneous equations ab + bc = 44 and ac + bc = 23 is

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Solution

The correct option is A
2

1.Given b . (a + c) = 44 ; c . (a + b) = 23 being a prime number.

∴ The given equations reduces to b . (a + c) = 44 ; a + b = 23.

The solutions are : b = 2, a = 21 and b = 22, a = 1.

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Similar questions

The number of ordered triples (a,b,c) of positive integers which satisfy the simultaneous equations ab + bc = 44 and ac + bc = 23 is

(a, b, c)

a b + b c = 44

a c + b c = 23

(a, b, c)

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{3} + 1 & a^{2} b & a^{2} c a b^{2} & b^{3} + 1 & b^{2} c a c^{2} & b c^{2} & c^{3} + 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 11

a - b + a b, b + c - b c

c - a - a c

2 c + a b - a c - b c

2 c - a b - a c - b c

2 c + a b + a c + b c

2 c - a b + a c + b c

a, b, c

log (1 + a c) = 2 k,

k