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Question

The sum of square of values of c for which the equations
2x+3y=3
(c+2)x+(c+4)y=(c+6)
(c+2)2x+(c+4)2y=(c+6)2 are consistent, is

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Solution

Given system of equations are consistent
Δ=0
Δ=∣ ∣ ∣233c+2c+4c+6(c+2)2(c+4)2(c+6)2∣ ∣ ∣=0

C1C1C3;C2C2C3∣ ∣ ∣10342c+64(2c+8)2(2c+10)(c+6)2∣ ∣ ∣=0∣ ∣ ∣10341c+68c+322c+10(c+6)2∣ ∣ ∣=0C1C14C2∣ ∣ ∣10301c+682c+10(c+6)2∣ ∣ ∣=0C3C33C1∣ ∣ ∣10001c+682c+10(c+6)2+24∣ ∣ ∣=0c210c=0c=0,c=10
Sum of squares of values of c is 0+100=100

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