Tell me the answer of Q.4
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Answer:
Step-by-step explanation:
Let the four parts be (a - 3d), (a - d), (a + d), (a + 3d).
(i) Given,Sum of four parts is 32.
⇒ a - 3d + a - d + a + d + a + 3d = 32
⇒ 4a = 32
⇒ a = 8
(ii) Product of extremes to means is 7:15
⇒ (a - 3d)(a + 3d)/(a - d)(a + d) = 7/15
⇒ 15(a - 3d)(a + 3d) = 7(a - d)(a + d)
⇒ 15[a² - 9d²] = 7[a² - d²]
⇒ 15a² - 135d² = 7a² - 7d²
⇒ 8a² = 128d²
⇒ 512 = 128d²
⇒ d² = 4
⇒ d = ±2
When a = 8, d = 2:
a - 3d = 2
a - d = 6
a + d = 10
a + 3d = 14
When a = 8, d = -2:
a - 3d = 14
a - d = 10
a + d = 6
a + 3d = 2
Therefore, the A.P is 2,6,10,14 (or) 14,10,6,2
Hope it helps!
Verified answer
Answer:
Step-by-step explanation:
Let the our parts are a-3d,a-d,a+d and a+3d.
Then by the given question,
a-3d+a-d+a+d+a+3d=32
or, 4a=32
or, a=8 and
(a-3d)(a+3d)/(a-d)(a+d)=7/15
or, a²-9d²/a²-d²=7/15
or, 15a²-135d²=7a²-7d²
or, 15a²-7a²=-7d²+135d²
or, 8a²=128d²
or, 8×8²=128d²
or, d²=8×8×8/128
or, d²=4
or, d=+-2
∴, The four parts are:
when d=2
8-(3×2)=8-6=2
8-2=6
8+2=10
8+(3×2)=14
when d=-2
8-(3×-2)=8+6=14
8-(-2)=8+2=10
8+(-2)=8-2=6
8+(3×-2)=8-6=2