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If 2b = a + c and y2 = xz, then what is xb - c yc - a za - b‑ equal to?
- a)3
- b)2
- c)1
- d)-1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If 2b = a + c and y2= xz, then what is xb - cyc - aza - bequal to?a)3b...
2b = a + c
∴ b - c = a - b
xb - c yc - a za - b = xb - c yc - a zb - c
⇒ (xz)b - c yc - a
⇒ (y2)b - c yc - a
⇒ (y)2b - c - a = y0 = 1
∴ b - c = a - b
xb - c yc - a za - b = xb - c yc - a zb - c
⇒ (xz)b - c yc - a
⇒ (y2)b - c yc - a
⇒ (y)2b - c - a = y0 = 1
Most Upvoted Answer
If 2b = a + c and y2= xz, then what is xb - cyc - aza - bequal to?a)3b...
To find the value of xb - cyc - aza - b, we need to substitute the given equations into the expression.
Given:
2b = ac
y^2 = xz
Substituting 2b = ac into the expression:
xb - cyc - aza - b
= xb - cyc - aza - 2b (since 2b = ac)
= xb - cyc - aza - ac
Now, let's substitute y^2 = xz into the expression:
= xb - cyc - aza - ac
= xb - cyc - aza - a(y^2/z) (since y^2 = xz)
= xb - cyc - aza - a(xy^2/z^2)
Now, let's simplify the expression further:
= xb - cyc - aza - a(xy^2/z^2)
= xb - a(xy^2/z^2) - cyc - aza
Now, we can factor out a common term:
= xb - a(xy^2/z^2) - cyc - aza
= xb - a(xy^2/z^2) - ac(y/z) - aza
= xb - a(xy^2/z^2) - ac(y/z) - a^2(z^2/a)
= xb - a(xy^2/z^2) - ac(y/z) - a^2z
Now, we can simplify further:
= xb - a(xy^2/z^2) - ac(y/z) - a^2z
= xb - a(xy^2/z^2) - a(y^2/z) - a^2z
= xb - a(xy^2/z^2) - ay - a^2z
Finally, we can factor out a common term from the first two terms:
= xb - a(xy^2/z^2) - ay - a^2z
= x(b - a(y^2/z^2)) - ay - a^2z
Therefore, the expression xb - cyc - aza - b is equal to x(b - a(y^2/z^2)) - ay - a^2z.
The correct answer is option C) 1.
Given:
2b = ac
y^2 = xz
Substituting 2b = ac into the expression:
xb - cyc - aza - b
= xb - cyc - aza - 2b (since 2b = ac)
= xb - cyc - aza - ac
Now, let's substitute y^2 = xz into the expression:
= xb - cyc - aza - ac
= xb - cyc - aza - a(y^2/z) (since y^2 = xz)
= xb - cyc - aza - a(xy^2/z^2)
Now, let's simplify the expression further:
= xb - cyc - aza - a(xy^2/z^2)
= xb - a(xy^2/z^2) - cyc - aza
Now, we can factor out a common term:
= xb - a(xy^2/z^2) - cyc - aza
= xb - a(xy^2/z^2) - ac(y/z) - aza
= xb - a(xy^2/z^2) - ac(y/z) - a^2(z^2/a)
= xb - a(xy^2/z^2) - ac(y/z) - a^2z
Now, we can simplify further:
= xb - a(xy^2/z^2) - ac(y/z) - a^2z
= xb - a(xy^2/z^2) - a(y^2/z) - a^2z
= xb - a(xy^2/z^2) - ay - a^2z
Finally, we can factor out a common term from the first two terms:
= xb - a(xy^2/z^2) - ay - a^2z
= x(b - a(y^2/z^2)) - ay - a^2z
Therefore, the expression xb - cyc - aza - b is equal to x(b - a(y^2/z^2)) - ay - a^2z.
The correct answer is option C) 1.
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