Gawanya mlinganyo mzima kwa mgawo wa x2, ambao ni 4.

Haya, nitakusaidia kutatua maswali haya. 1. Tatua 4x^2 - 16x - 9 = 0 kwa kutumia njia ya kukamilisha mraba. Step 1: Gawanya mlinganyo mzima kwa mgawo wa x^2, ambao ni 4. x^2 - 4x - (9)/(4) = 0 Step 2: Hamisha nambari isiyobadilika (constant term) upande wa kulia. x^2 - 4x = (9)/(4) Step 3: Kamilisha mraba upande wa kushoto. Ongeza ((-4)/(2))^2 = (-2)^2 = 4 pande zote mbili. x^2 - 4x + 4 = (9)/(4) + 4 x^2 - 4x + 4 = (9)/(4) + (16)/(4) (x - 2)^2 = (25)/(4) Step 4: Chukua mzizi wa mraba pande zote mbili. sqrt((x - 2)^2) = ±sqrt((25)/(4)) x - 2 = ±(5)/(2) Step 5: Tatua kwa x. x = 2 ± (5)/(2) Kuna suluhisho mbili: x_1 = 2 + (5)/(2) = (4)/(2) + (5)/(2) = (9)/(2) x_2 = 2 - (5)/(2) = (4)/(2) - (5)/(2) = -(1)/(2) Jibu la mwisho ni: x = (9)/(2) au x = -(1)/(2) 2. Vipimo vya kitabu cha mazoezi ni 36.8cm na 30.5cm. Kokotoa tofauti inayowezekana kati ya vipimo hivyo viwili. Step 1: Tambua vipimo vilivyotolewa. Kipimo cha kwanza ni 36.8cm. Kipimo cha pili ni 30.5cm. Step 2: Tafuta tofauti kwa kutoa kipimo kidogo kutoka kwa kikubwa. Tofauti = 36.8cm - 30.5cm Tofauti = 6.3cm Jibu la mwisho ni: 6.3cm 3. Tatua kwa x katika mlinganyo (_5 x)^2 + _5 x = 2. Step 1: Acha y = _5 x. Badilisha y kwenye mlinganyo. y^2 + y = 2 Step 2: Panga upya mlinganyo kuwa mlinganyo wa quadratic. y^2 + y - 2 = 0 Step 3: Tatua mlinganyo wa quadratic kwa y. Unaweza kutumia factorization. (y + 2)(y - 1) = 0 Hivyo, y + 2 = 0 au y - 1 = 0. y = -2 au y = 1. Step 4: Badilisha _5 x kurudi kwa y na utatue kwa x. Kesi ya 1: y = -2 _5 x = -2 Kwa kutumia ufafanuzi wa logarithm (b^y = x), tunapata: x = 5^-2 x = (1)/(5^2) x = (1)/(25) Kesi ya 2: y = 1 _5 x = 1 x = 5^1 x = 5 Step 5: Hakikisha suluhisho ni halali (argument ya logarithm lazima iwe chanya). Kwa x = (1)/(25), _5 ((1)/(25)) ni halali. Kwa x = 5, _5 (5) ni halali. Jibu la mwisho ni: x = (1)/(25) au x = 5 4. Fanya x kuwa mada ya fomula (a^2)/(x) = a sqrt((x^2 - m)/(m)). Step 1: Gawanya pande zote mbili kwa a (kwa kudhani a ≠ 0). (a)/(x) = sqrt((x^2 - m)/(m)) Step 2: Piga mraba pande zote mbili ili kuondoa mzizi wa mraba. ((a)/(x))^2 = (sqrt((x^2 - m)/(m)))^2 (a^2)/(x^2) = (x^2 - m)/(m) Step 3: Zidisha msalaba. a^2 m = x^2 (x^2 - m) a^2 m = x^4 - mx^2 Step 4: Panga upya mlinganyo ili kuleta x^2 pamoja. x^4 - mx^2 - a^2 m = 0 Huu ni mlinganyo wa quadratic kwa x^2. Acha u = x^2. u^2 - mu - a^2 m = 0 Tumia fomula ya quadratic u = -b ± sqrt(b^2 - 4ac)2a ambapo a=1, b=-m, c=-a^2m. u = -(-m) ± sqrt((-m)^2 - 4(1)(-a^2 m))2(1) u = m ± sqrt(m^2 + 4a^2 m)2 u = m ± sqrt(m(m + 4a^2))2 Step 5: Badilisha x^2 kurudi kwa u. x^2 = m ± sqrt(m(m + 4a^2))2 Kwa kuwa x^2 lazima iwe chanya, tunachukua ishara chanya ya mzizi wa mraba. x^2 = m + sqrt(m(m + 4a^2))2 (Tunadhania m > 0 na m + 4a^2 > 0 ili mzizi wa mraba uwe halisi na x^2 iwe chanya). Step 6: Chukua mzizi wa mraba pande zote mbili ili kupata x. x = ±sqrt(m + m(m + 4a^2))2 Jibu la mwisho ni: x = ±sqrt(m + m(m + 4a^2))2 Tuma swali linalofuata 📸