Answered

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SOLVE THE FF. QUADRATIC EQUATIONS AND GIVE THEIR FOLLOWING PROPERTIES.AND ANSWER THE QUESTIONS THAT FOLLOW.
1.x^2=16
2.t^2=81
3.r^2-100=0
4.x^2-144=0
5.2s^2=50
6.4x^2-225=0
7.3h^2-147=0
8.(x-4)^2=169
9.(k+7)^2=289
10.(2s-1)^2=225

questions:
1.how did you find the solutions of each equation?
2.What mathematics concepts or principles did you apply in finding the solutions?explain how you applied these.

Sagot :

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1. x²-16=0 ; (x+4)(x-4)=0 ; x=4 or -4
2. t²-81=0 ; (t+9)(t-9)=0 ; t=9 or -9
3. r²-100=0 ; (r+10)(r-10)=0 ; r=10 or -10
4. x²-144=0 ; (x+12)(x-12)=0 ; x=12 or -12
5. 2s²-50=0 ; s²-25=0 ; (s+5)(s-5)=0 ; s=5 or -5
6. 4x²-225=0 ; (2x-15)(2x+15)=0 ; x=7.5 or -7.5
7. 3h²-147=0 ; h²-147/3=0 ; (h+√[147/3])(h-√[147/3])=0 ; (h+√49)(h-√49)=0  ;  
(h+7)(h-7)=0 ; h=7 or -7
8.(x-4)²-169=0 ; (x-4-13)(x-4+13)=0 ; (x-17)(x+9)=0 ; x=17 or -9
9. (k+7)²-289=0 ; (k+7-17)(k+7+17)=0 ; (k-10)(k+24)=0 ; k=10 or -24
10. (2s-1)²-225=0 ; (2s-1+15)(2s-1-15)=0 ; (2s+14)(2s-16)=0 ; s=-7 or 8

1. Through the difference of two squares. a²-b²=(a+b)(a-b).
2. Difference of two squares.
1. X²= 16 X²=√16 X²= 4 2. T²=81 T²=√81 T²= 9 3. r²-100=0 r-√100=0 r=±10 4. x²-144=0 x-√144=0 x=±12