Let x₁, x₂, x₃, x₄ be the solution of the equation 4 x^4+8 x^3-17 x^2-12 x+9=0 and (4+x₁^2 ) (4+x₂^2 ) (4+x₃^2 ) (4+x₄^2 )= 125 16 m . Then the value of m is

Step-by-step solution

aligned & 4 x^4+8 x^3-17 x^2-12 x+9 & =4 (x-x₁ ) (x-x₂ ) (x-x₃ ) (x-x₄ ) aligned Put x=2 i &-2 i aligned & 64-64 i+68-24 i+9= (2 i-x₁ ) (2 i-x₂ ) (2 i-x₃ ) & (2 i-x₄ ) & =141-88 i ....(1) & 64+64 i+68+24 i+9=4 (-2 i-x₁ ) (-2 i-x₂ )(-2 i & .-x₃ ) (-2 i-x₄ ) & =141+88 i....(2) aligned aligned & 125 16 ~m = 141^2+88^2 16 & ~m =221 aligned