The given expression is
c=y16x+x49y, where
x and
y are non-zero real numbers. We need to determine which of the given values
−70,
60,
−50, and
−60 cannot be taken by
c. First, let's simplify the expression:
c=xy16x2+49y2 Now, we can rewrite the expression as:
c=xy16x2+xy49y2=16(yx)+49(xy)=16k+k49 Where
k=yx. Since
x and
y are real and non-zero,
k is also real. We can now create a quadratic equation in terms of
k:
16k2−ck+49=0 For
k to be real, the discriminant of this quadratic equation must be greater than or equal to
0:
c2−4⋅16⋅49≥0 c2−3136≥0 Solving for
c, we get:
∣c∣≥56 This means that the absolute value of
c must be greater than or equal to
56. Therefore,
c cannot take the value
−50, as
∣−50∣=50<56. So, out of the given options,
c cannot take the value
−50.