Monchichi
Answered

Maligayang pagdating sa Imhr.ca, ang pinakamahusay na platform ng tanong at sagot para sa mabilis at tumpak na mga sagot. Tuklasin ang komprehensibong mga solusyon sa iyong mga tanong mula sa isang malawak na hanay ng mga propesyonal sa aming madaling gamitin na platform. Kumuha ng detalyado at eksaktong sagot sa iyong mga tanong mula sa dedikadong komunidad ng mga eksperto sa aming Q&A platform.

1. ( ____x² + ____x + 1) - (7x² + ____x + ____) = - 5x² - 14​

Sagot :

Amaranthaceae

Answer:

[tex] \bold{( \underline{2x}^2+ \underline{2}x+1)-(7x^2+ \underline{2}x+ \underline{15})=-5x^2-14} \\ [/tex]

Step-by-step explanation:

To explain how to approach this question, I am going to place letters in the blank spaces:

[tex] \quad \sf{(ax^2+bx+c)-(dx^2+ex+f)=-5x^2-14} \\ [/tex]

First, compare the coefficients of the x² terms on both sides of the equation:

[tex] \implies\: \sf{a - d = -5a−d=−5} \\ [/tex]

Therefore, we need to choose any two numbers in place of a and d whose difference is -5:

[tex]\sf\implies \: a = 2 \: and \: d = 7 \: as \: 2 - 7 = -5 \\ [/tex]

Similarly, upon comparing the coefficients of the x terms, we can see that there is no x term on the right side of the equation. Therefore, we need to choose numbers in place of b and e for which the difference is zero. So b and e should be the same number:

[tex]\sf\implies \: b = 2 \: and \: e = 2 \: as \: 2 - 2 = 0\\ [/tex]

Finally, compare the constant term on both sides of the equation:

[tex]\implies\: \sf{c - f = -14c−f=−14} \\ [/tex]

Therefore, we need to choose any two numbers in place of c and f whose difference is -14:

[tex] \sf \implies \: {c = 1 \: and \: f = 15 \: as \: 1 - 15 = -14} \\ [/tex]

Plug in the numbers in place of the letters on the left side of the equation:

[tex] \implies \: \underline{ \bold{(2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14}} \\ [/tex]

[tex] \\ \large \sf{\pmb{Checking} : } \\ [/tex]

[tex] \sf{Remove \: the \: brackets:} \\ [/tex]

[tex] \sf \implies \: {2x^2+2x+1-7x^2-2x-15=-5x^2-14} \\ [/tex]

[tex] \sf {Collect \: like \: terms:} \\ [/tex]

[tex] \sf \implies \: {2x^2-7x^2+2x-2x+1-15=-5x^2-14} \\ [/tex]

[tex] \sf{Combine \: like \: terms:} \\ [/tex]

[tex] \sf \implies \: {-5x^2-14=-5x^2-14} \\ \\ [/tex]

Hence proving that the left and right sides of the equation are the same.

Umaasa kami na nakatulong ito. Mangyaring bumalik kapag kailangan mo ng higit pang impormasyon o mga sagot sa iyong mga katanungan. Pinahahalagahan namin ang iyong pagbisita. Lagi kaming narito upang mag-alok ng tumpak at maaasahang mga sagot. Bumalik anumang oras. Maraming salamat sa pagbisita sa Imhr.ca. Balik-balikan kami para sa pinakabagong mga sagot at impormasyon.