a (3x+4)² square meter land, and (5x-7)² square meter land. which land will you choose

Answer 1

(3x+4)^2 = 9x^2 +24x +16

(5x-7)^2 = 25x^2 -70x + 49

25x^2 -70x +49 = 9x^2 +24x + 16

16x^2 -94x + 33 = 0

x = 94/32 +/-(1/32)sqr(94^2-48(33))

x = [(94 +/- sqr(8836-1584)]/32

x= [94+/-sqr7252]/32

x= about (94+/-85.16)/32

x= 8.84/32 or 179.16/32

x= about 0.28 or 5.60

those are the dividing points of intervals of which is better or worse

x> 5.6 and the 2nd is larger (5x-7)^2 is larger area

for 0.28 < x < 5.60, (3x+4)^2 is the larger area

for x< 0.28, (5x-7)^2) is the larger area''

test it by trying a couple simple integers

let x= 1,

then x= 0,

x=6

3

x=1, then (5-7)^2 = 4 < (3x+4)^2 =4< 49: (3x+4)^2 has greater area for ,26<x < 5.8

x=0 then 1<49

x=6, then 23^2>22^2: (5x-7)^2 has greater area for x>5.8 or for x<.26 rounded off to two decimals

something like that. no guarantees of arithmetic mistake(s) somewhere above, but it's the basic method.