Question:`(x - 3x + 2)/(x^2 - 4x + 3), (x^2 - 5x + 6)/(x^2 - 7x + 12), (x^2 - 16)/(x^2 - 9)` তিনটি বীজগাণিতীয় রাশি। ক. ৩য় রাশির লব ও হরের পার্থক্য কত? খ. রাশি তিনটির গুণফল কত? গ. ১ম রাশি `-: `২য় রাশি `xx` ৩য় রাশি = কত?
Answer ক. দেওয়া আছে, ৩য় রাশির লব` = x^2 - 16` এবং ৩য় রাশির হর = `x^2 - 9` :. পার্থক্য `= (x^2 - 16)^2 - (x^2 - 9)^2` `(x^2)^2 - 2.x^2.16 + (16)^2 - {(x^2)^2 - 2.x^2.9 + 9^2}` `= x^4 - 32x^2 + 256 - x^4 + 18x^2 - 81` `= - 14x^2 + 175` `= 175 - 14x^2` খ. নির্ণেয় গুণফল `= (x^2 - 3x + 2)/(x^2 - 4x + 3) xx (x^2 - 5x + 6)/(x^2 - 7x + 12) xx (x^2 - 16)/(x^2 - 9)` `= (x^2 - 2x - x + 2)/(x^2 - 3x - x + 3) xx (x^2 - 3x - 2x + 6)/(x^2 - 4x - 3x + 12) xx (x^2 - 4^2)/(x^2 - 3^2)` `= (x(x - 2) - 1(x - 2))/(x(x - 3) - 1(x - 3)) xx (x(x - 3) - 2(x - 3))/(x(x - 4) - 3(x - 4)) xx ((x + 4)(x - 4))/((x + 3) (x - 3))` `= ((x - 2)(x - 1))/((x - 3)(x - 1)) xx ((x - 3)(x - 2))/((x - 4)(x - 3)) xx ((x + 4)(x - 4))/((x + 3)(x - 3))` `= ((x - 2)(x - 2)(x + 4))/((x - 3)(x + 3)(x - 3))` `= ((x - 2)^2(x + 4))/((x - 3)^2 (x + 3))` উত্তর: `((x - 2)^2(x + 4))/((x - 3)^2 (x + 3))` গ. `(x^2 - 3x + 2)/(x^2 - 4x + 3) -: (x^2 - 5x + 6)/(x^2 - 7x + 12) xx (x^2 - 16)/(x^2 - 9)` `= (x^2 - 2x - x + 2)/(x^2 - 3x - x + 3) -: (x^2 - 3x - 2x + 6)/(x^2 - 4x - 3x + 12) xx (x^2 - 4^2)/(x^2 - 3^2)` `= (x(x - 2) - 1(x - 2))/(x(x - 3) - 1(x - 3)) -: (x(x - 3) - 2(x - 3))/(x(x - 4) - 3(x - 4)) xx ((x + 4)(x - 4))/((x + 3)(x - 3))` `= ((x - 2)(x - 1))/((x - 3)(x - 1)) -: ((x - 3)(x - 2))/((x - 4)(x - 3)) xx ((x + 4)(x - 4))/((x + 3)(x - 3))` `= ((x - 2)(x - 1))/((x - 3)(x - 1)) xx ((x - 4)(x - 3))/((x - 3)(x - 2)) xx ((x + 4)(x - 4))/((x + 3)(x - 3))` `= ((x - 4)^2 (x + 4))/((x - 3)^2 (x + 3))`
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`(x - 3x + 2)/(x^2 - 4x + 3), (x^2 - 5x + 6)/(x^2 - 7x + 12), (x^2 - 16)/(x^2 - 9)` tinti bijoganitiy rashi. ka. ৩y rashir lbo o horer parothokjkoto? kh. rashi tintir gunphol koto? ga. ১mo rashi `-: `২y rashi `xx` ৩y rashi = koto?