Answer:
12.33
Explanation:
To obtain the value of 137m + 137n, let us calculate the value of m and n.
NOTE: m and n are the solutions to the equation: 685x² – 58x – 976 = 0
Thus, we can obtain the solutions to equation by doing the following:
685x² – 58x – 976 = 0
a = 685
b = – 58
c = – 976
Using formula method:
x = – b ± √(b² – 4ac) ÷ 2a
x = – (–58) ± √(–58² – 4×685×–976) ÷ 2 × 685
= 58 ± √(3364 – – 2674240) ÷ 1370
= 58 ± √(3364 + 2674240) ÷ 1370
= 58 ± √(2677604) ÷ 1370
= 58 ± 1636.3386 / 1370
= (58 + 1636.3386) / 1370 or (58
– 1636.3386) / 1370
= 1694.3386 / 1370 or – 1578.3386/1370
x = 1.24 or –1.15
Thus,
m = 1.24
n = –1.15
Finally, we can obtain the value of
137m + 137n as shown below:
137m + 137n
m = 1.24
n = –1.15
= (137 × 1.24) + (137 × – 1.15)
= 169.88 + (– 157.55)
= 169.88 – 157.55
= 12.33
Thus, the value of 137m + 137n is 12.33