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Question:

If∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔, thenais equal to𕒶924�If∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔, thenais equal to𕒶924�∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵x2+xx+1x𕒶x2+xx2+xx2xxx222++xxx+1x+1xx++11x𕒶x𕒶xx−𕒶22x2+3x󔼕x3x󔼨x2+3x󔼔x2+3x�x2xxx222++33xx−�x3x33xx3x󔼩x�xx−󔼩x2+2x+32x󔼔x𕒵x2+2x+3x2+2x+3x2xxx222++22xx++332x󔼔x�xx−�x󔼔x�xx−󔼓∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣==aaxx−�aaaaa𕒶9𕒶9𕒶9𕒶9−𕒶929242424242424󔼨󔼨󔼨󔼨−�A𕒶9𕒶9𕒶9𕒶9𕒶9−𕒶929B󔼨󔼨󔼨󔼨󔼨−�C21212121212121D24242424242424?

𕒶9

󔼨

21

24

Solution:

Given,∣∣∣∣∣x2+xx+1x𕒶2x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔R1⟶R1+R3∣∣∣∣∣2x2+3x+33x3x󔼨x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔R1⟶R1−R2∣∣∣∣∣4002x2+3x󔼕x3x𕒷x2+2x+32x󔼔x𕒵∣∣∣∣∣=ax󔼔⇒4[6x2𕒷x𕒺x2+6x+3x𕒷]=ax󔼔⇒24x󔼔=ax󔼔On comparing, we geta=24