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ORFind four Numbers in A.P. such that the sum of 2nd and 3rd terms is 22andthe product of 1st and 4th term is 85.51. In an equilateral triangle ABCD is a point on BC, such thatBD ==BC. Prove that 9AD2 = 7AB23B.ORBL and CM are medians of a triangle ABC,|A=90° Prove that 4(BL2 + CM2) = 5BC2​

Answer»

Step-by-step EXPLANATION:

T2+T3=22

a+d+a+2d=22

2a+3d=22

3d=22-2a

a(a+3d)=85

a^2+3ad=85

a^2+a(22-2a)=85

a^2+22a-2a^2=85

22a-a^2=85

a^2-22a+85=0

a^2-(17+5)a+85=0

a^2-17a-5a+85=0

a(a-17)-5(a-17)=0

a=5 or 17

if a=5

3d=22-10

d=4

if a=17

3d=22-34

d=-4

if a=5 and d=4

Ap=5,9,13,17......

if a=17 and d=-4

Ap=17,13.9.5....

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