Question

2/3,3/4 are rhe solution of the equation 12x2-17x+6=0 or not

Answer 1

2/3, 3/4=1/2 and 12×2-17×+6=78

Answer 2

Question :- Determine whether x=2/3 and x=3/4 are solutions of the equation 12x² - 17x + 6 = 0 ?

Solution :-

we know that, if x is a solution of any equation . then,

f(x) = 0 .

checking at x = (3/4) now :-

→ f(x) = 12x² - 17x + 6

→ f(3/4) = 12(3/4)² - 17(3/4) + 6

→ f(3/4) = 12(9/16) - (51/4) + 6

→ f(3/4) = (27/4) - (51/4) + 6

→ f(3/4) = (27 - 51 + 24)/4

→ f(3/4) = (51 - 51)/4

→ f(3/4) = 0/4

→ f(3/4) = 0 .

Therefore, x = 3/4 is a solution of given equation .

checking at x = (2/3) now :-

→ f(x) = 12x² - 17x + 6

→ f(3/4) = 12(2/3)² - 17(2/3) + 6

→ f(3/4) = 12(4/9) - (34/3) + 6

→ f(3/4) = (16/3) - (34/3) + 6

→ f(3/4) = (16 - 34 + 18)/3

→ f(3/4) = (34 - 34)/3

→ f(3/4) = 0/3

→ f(3/4) = 0 .

Therefore, x = 2/3 is a solution of given equation.

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