Mutiso owns a rectangular farm with area (x2-6x+9) m2. Factorise to find the length of one side.

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ScanSolve AI Tutor · Accepted Answer

Haya hapa masuluhisho ya swali uliyotuma:

Swali: Mutiso anamiliki shamba la mstatili lenye eneo la $(x^2 - 6x + 9)m^2$ . Factoriza ili kupata urefu wa upande mmoja.

Tambua usemi wa eneo.
Eneo la shamba ni $x^2 - 6x + 9$ .
Factoriza usemi wa quadratic.
Usemi $x^2 - 6x + 9$ ni trinomial kamili ya mraba. Inaweza kuandikwa kama $(a-b)^2 = a^2 - 2ab + b^2$ .
Hapa, $a^2 = x^2 \implies a = x$ .
Na $b^2 = 9 \implies b = 3$ .
Angalia muda wa kati: $-2ab = -2(x)(3) = -6x$ .
Hii inalingana na usemi uliotolewa.
Hivyo, $x^2 - 6x + 9 = (x-3)(x-3) = (x-3)^2$ .
Bainisha urefu wa upande mmoja.
Kwa kuwa eneo la shamba ni $(x-3)^2$ , inamaanisha shamba hilo ni mraba, na urefu wa kila upande ni $(x-3)$ .

Jibu: Urefu wa upande mmoja ni $(x-3) \text{ m}$

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