Question

If a,b,c,d are in proportion,prove that:
(5a + 7b)(2c - 3d) = (5c + 7d)(2a - 3b)
please answer......
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Answer 1

Given: a,b,c,d are in proportion.

To find: prove that:   (5a + 7b)(2c - 3d) = (5c + 7d)(2a - 3b)

Solution:

• Now we have given that a,b,c,d are in proportion , so:

               ad = bc

• Now  lets consider LHS, we have:

               ( 5a + 7b )( 2c - 3d )

• Expanding it, we get:

               10ac - 15ad + 14bc - 21bd

                10ac - 21bd  ad

• Now lets consider RHS, we have:

                ( 5c + 7d ) ( 2a - 3b )  

                10ac - 15bc + 14ad - 21bd

                10ac - 21bd - ad

• LHS = RHS

• Hence proved.

Answer:

             So we proved that  (5a + 7b)(2c - 3d) = (5c + 7d)(2a - 3b)